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Logarithms — MATHEMATICS STD 9 — Question

ICSE BoardEnglish MediumSTD 9MATHEMATICSLogarithms1 Mark
Question
State, true or false $:\ $ If $\frac{\log 25}{\log 5}=\log x_t$ then $\mathrm{x}=2$
✓

Answer

Given that
$\frac{\log 25}{\log 5}=\log \mathrm{x}$
$ \Rightarrow \frac{\log 5 \times 5}{\log 5}=\log \mathrm{x}$
$ \Rightarrow \frac{\log 5^2}{\log 5}=\log x$
$ \Rightarrow \frac{2 \log 5}{\log 5}=\log x \ldots\left[\log _a m^n=n \log _a m\right]$
$ \Rightarrow 2=\log { }_{10} \mathrm{x}$
$ \Rightarrow 10^2=\mathrm{x}$
$ \Rightarrow \mathrm{x}=100$
Thus, the statement, $x=2$ is false.

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