Question 512 Marks
Convert each of the to logarithmic form :
$6^0=1$
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Convert each of the to logarithmic form :
$5^2=25$
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Convert each of the to logarithmic form :
$4^{-1}=\frac{1}{4}$
Answer$\log _4 \frac{1}{4}=-1$
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Convert each of the to logarithmic form :
$3^{-3}=\frac{1}{27}$
Answer$\log _3\left(\frac{1}{27}\right)=-3$
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Convert each of the to logarithmic form :
$10^{-2}=0.01$
Answer$\log _{10}(0.01)=-2$
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Convert each of the to exponential form:
$\log _a 1=0$
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Convert each of the to exponential form:
$\log _8 4=\frac{2}{3}$
Answer$(8)^{\frac{2}{3}}=4$
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Convert each of the to exponential form:
$\log _5\left(\frac{1}{5}\right)^3=-1$
Answer$5^{-1}=\frac{1}{5}$
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Convert each of the to exponential form:
$\log _3 81=4$
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Convert each of the to exponential form:
$\log _2 \frac{1}{8}=-3$
Answer$2^{-3}=\frac{1}{8}$
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Convert each of the to exponential form:
$\log _{10}(0.01)=-2$
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Express each of as a single logarithm:
$1-\frac{1}{3} \log _{10} 64$
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Express each of as a single logarithm:
$2 \log _{10}\left(\frac{11}{13}\right)+\log _{10}\left(\frac{130}{77}\right)-\log _{10}\left(\frac{55}{91}\right)$
View full question & answer→Question 642 Marks
Express each of as a single logarithm:
$\frac{1}{2} \log _{10} 9+\frac{1}{4} \log _{10} 81+2 \log _{10} 6-\log _{10} 12$
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Express each of as a single logarithm:
$2+\frac{1}{2} \log _{10} 9-2 \log _{10} 5$
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Express each of as a single logarithm:
$2 \log _{10} 5+2 \log _{10} 3-\log _{10} 2+1$
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Express each of as a single logarithm:
$2 \log _{10} 8+\log _{10} 36-\log _{10}(1.5)-3 \log _{10} 2$
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Write the logarithmic equation for :
$x=a b \sqrt{\frac{a-b}{a+b}}$
Answer$\log x=\log a+\log b+\frac{1}{2}[\log (a-b)-\log (a+b)]$
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Write the logarithmic equation for :
$R =\sqrt{\frac{3 V}{\pi h}}$
Answer$\log R=\frac{1}{2}(\log 3+\log V-\log \pi-\log h)$
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If $\left(\log 7-\log 2+\log 16-2 \log 3-\log \frac{7}{45}\right)=1+\log n$, find the value of $n$.
[Hint: $R H S=\log 10+\log n=\log (10 n)$.
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Solve for $x$ :
$\frac{\log x}{\log 5}=\frac{\log 9}{\log \left(\frac{1}{3}\right)}$
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Solve for $x$ :
$2 \log x+1=\log 250$
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Solve for $x$ :
$\log \left(x^2-21\right)=2$
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Solve for $x$ :
$\log (x+3)-\log (x-3)=1$
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Solve for $x$
:$\log (x+4)-\log (x-4)=\log 2$
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Solve for $x$ :
$\log (x+2)+\log (x-2)=\log 5$
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If $\log 27=1.4313$, find the value of: $\log 30$
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If $\log 27=1.4313$, find the value of: $\log 9$
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If $\log 8=0.9030$, find the value of $:$ $\log (0.125)$
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If $\log 8=0.9030$, find the value of $:$$\log \sqrt{32}$
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If $\log 8=0.9030$, find the value of $:$$\log 4$
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If $\log 2=0.3010$, find the value of $\left(\log \frac{75}{16}-2 \log \frac{5}{9}+\log \frac{32}{243}\right)$.
View full question & answer→Question 832 Marks
Given $: \log 2=0.3010$ and $\log 3=0.4771$, find the value of : $\log \left(\frac{9}{4}\right)$
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Given $: \log 2=0.3010$ and $\log 3=0.4771$, find the value of : $\log \sqrt{18}$
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Given $: \log 2=0.3010$ and $\log 3=0.4771$, find the value of : $\log 25$
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Given $: \log 2=0.3010$ and $\log 3=0.4771$, find the value of : $\log 12$
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Express $\log _{10}\left(\frac{\sqrt{p q^3}}{r^2 s}\right)$ in terms of $\log _{10} p, \log _{10} q, \log _{10} r$ and $\log _{10} s$.
Answer$\frac{1}{2}\left(\log _{10} p+3 \log _{10} q\right)-2 \log _{10} r-\log _{10} s$
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Express $\log _{10}\left(\frac{x^2 y^3}{z}\right)$ in terms of $\log _{10} x, \log _{10} y$ and $\log _{10} z$.
Answer$2 \log _{10} x+3 \log _{10} y-\log _{10} z$
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Evaluate:
$\log \frac{81}{8}+2 \log \frac{2}{3}-3 \log \frac{3}{2}+\log \frac{3}{4}$
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Evaluate:
$3 \log 2-\frac{1}{3} \log 27+\log 12-\log 4+3 \log 5$
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Evaluate:
$\log 5+16 \log \left(\frac{625}{6}\right)+12 \log \left(\frac{4}{375}\right)+7 \log \left(\frac{81}{1250}\right)$
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Given (log _{10} x=a, log _{10} y=b),If $\log _{10} P =2 a-b$, express P in terms of $x$ and $y$.
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Given (log _{10} x=a, log _{10} y=b),Write down $10^{2 b}$ in terms of $y$.
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Given $\log _{10} x=a, \log _{10} y=b$, Write down $10^{a+1}$ in terms of $x$.
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Find the value of $x$, when:
$\log _x(0.008)=-3$
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Find the value of $x$, when:
$\log _2\left(x^2-9\right)=4$
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Find the value of $x$, when:
$\log _x 64=\frac{3}{2}$
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Find the value of $x$, when:
$\log _5\left(x^2-19\right)=3$
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Find the value of $x$, when:
$\log _{\sqrt{3}}(x-1)=2$
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Find the value of $x$, when:
$\log _3 x=0$
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