Question

Log 225/log 15 = log x

Answer 1

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Answer 2

The value of x = 100

Given :

$\displaystyle \sf{ \frac{log \: 225}{log \: 15} = log \: x }$

To find :

The value of x

Formula :

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

Solution :

Step 1 of 2 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ \frac{log \: 225}{log \: 15} = log \: x }$

Step 2 of 2 :

Find the value of x

$\displaystyle \sf{ \frac{log \: 225}{log \: 15} = log \: x }$

$\displaystyle \sf{ \implies \frac{log \: {15}^{2} }{log \: 15} = log \: x }$

$\displaystyle \sf{ \implies \frac{2 \: log \: {15}^{} }{log \: 15} = log \: x }\: \: \: \bigg[ \: \because \:log( {a}^{n} ) = n log(a) \bigg]$

$\displaystyle \sf{ \implies 2 = log \: x }$

$\displaystyle \sf{ \implies log \: x = 2 }$

$\displaystyle \sf{ \implies log_{10}(x) = 2 }\: \: \: \bigg[ \: \because \:base \: is \: taken \: as \: 10 \bigg] \:$

$\displaystyle \sf{ \implies x = {10}^{2} }$

$\displaystyle \sf{ \implies x = 100}$

Hence the required value of x = 100

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