Question

Prove :
$log_{10}(125) = 3(1 - log_{10}2)$
​

Answer 1

Given :

• $log_{10}(125) = 3 ( 1 - log_{10}2 )$

To find :

• $log_{10}(125) = 3 ( 1 - log_{10}2 )$

According to the question :

⟹ $log_{10}(125) = 3 ( 1 - log_{10}2 )$

⟹ $log_{10}[ 125 - 3 ] ( 1 - log_{10^2} ) = x$

⟹ $log_{10} 125 - 3 + log_{10^8} = x$ ... $( log a^b = b\:log\:a )$

⟹ ∴ $log_{10} [125] - 3 log_{10} 10 + log_{10^8} = x$

⟹ $( log \frac{a}{b} = log\:a - log\:b )$

⟹ ∴ $x = log_{10} \frac{( 125 × 8 )}{1000} = log_{10^1}$

⟹ $\bold{0}$

More information :

✎ To solve these type of problems, we need to know the formulas .

✎ Must know how to solve these type of exponential equations .

✎ Then substituting the values .

So, It's Done !!