Logarithms - ICSE STD 9 MATHEMATICS Questions

Q 1[1 Mark Question Answer]1 Mark

Express the following in terms of $\ \log 5$ and or $\log 2: \log 125$

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Q 2[1 Mark Question Answer]1 Mark

If $\log _{10}x = p$, express the following in terms of $x : 10^p$

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Q 3[1 Mark Question Answer]1 Mark

Express the following in the exponential form$:-2 = \log_2 0.25$

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Q 4[1 Mark Question Answer]1 Mark

Express the following in the exponential form$:q = \log_a p$

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Q 5[1 Mark Question Answer]1 Mark

Express the following in the exponential form$:\log _{25} \sqrt{5}=\frac{1}{4}$

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Q 6[2 Mark Question Answer]2 Marks

Express $\log_{10}3 + 1$ in terms of $\log_{10}x.$

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Q 7[2 Mark Question Answer]2 Marks

Solve for $x : \frac{\log 81}{\log 9}= x$

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Q 8[2 Mark Question Answer]2 Marks

Solve for $x : \frac{\log 27}{\log 243}= x$

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Q 9[2 Mark Question Answer]2 Marks

Solve for $x: \log (x + 5) = 1$

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Q 10[2 Mark Question Answer]2 Marks

If $a b + b \log a - 1 = 0,$ then prove that $b^a.a^b = 10$

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Q 11[3 marks sum]3 Marks

Solve for $x : \frac{\log 289}{\log 17}=\log x$

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Q 12[3 marks sum]3 Marks

Solve for $x : \frac{\log 1331}{\log 11}=\log x$

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Q 13[3 marks sum]3 Marks

Solve for $x : \frac{\log 128}{\log 32}= x$

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Q 14[3 marks sum]3 Marks

Solve for $x : \frac{\log 125}{\log 5}=\log x$

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Q 15[3 marks sum]3 Marks

Solve for $x : \frac{\log 121}{\log 11}=\log x$

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Q 16[4 marks sum]4 Marks

$\log _2 x+\log _4 x+\log _{16} x=\frac{21}{4}$

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Q 17[4 marks sum]4 Marks

Solve the following:$\log _4 x+\log _4(x-6)=2$

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Q 18[4 marks sum]4 Marks

Simplify the following:$12 \log \frac{3}{2}+7 \log \frac{125}{27}-5 \log \frac{25}{36}-7 \log 25+\log \frac{16}{3}$

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Q 19[4 marks sum]4 Marks

Simplify the following:$2 \log 7+3 \log 5-\log \frac{49}{8}$

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Q 20[4 marks sum]4 Marks

Simplify the following:$2 \log 5+\log 8-\frac{1}{2} \log 4$

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Q 21[5 marks sum]5 Marks

Simplify the following:$3 \log \frac{32}{27}+5 \log \frac{125}{24}-3 \log \frac{625}{243}+\log \frac{2}{75}$

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Q 22[5 marks sum]5 Marks

Prove that: $\frac{1}{\log _8 36}+\frac{1}{\log _9 36}+\frac{1}{\log _{18} 36}=2$

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Q 23[5 marks sum]5 Marks

Prove that: $\frac{1}{\log _2 30}+\frac{1}{\log _3 30}+\frac{1}{\log _5 30}=1$

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Q 24[5 marks sum]5 Marks

Find the value of:$\frac{\log \sqrt{27}+\log 8+\log \sqrt{1000}}{\log 120}$

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Q 25[5 marks sum]5 Marks

If $2 \log x + 1 = \log$ $360$, find: $\log (3 x^2 - 8)$

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Q 26TRUE / FALSE1 Mark

If $\frac{\log 49}{\log 7}=\log y$, then $y=100$

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Q 27TRUE / FALSE1 Mark

State, true of false$:\ \log_ba =-\log_ab$

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Q 28TRUE / FALSE1 Mark

State, true of false:
log 4 x log 1 = 0

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Q 29TRUE / FALSE1 Mark

State, true of false$:\ \log (x + y) = \log xy$

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Q 30TRUE / FALSE1 Mark

If $\log _2 8=3$, then $\log _8 2=\frac{1}{3}$

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Logarithms question types

Logarithms questions

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Logarithms MATHEMATICS - Logarithms

Logarithms question types

Logarithms questions

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