Question

If x power 1-log x base 5=0.04,then among the following,correct statement is a)1by5 b)5 c)1by25 d)35

Answer 1

$\underline{\textsf{We have to find the value of x here}}\bold{:}$

$\mathsf{Now,\:x^{1-log_{5}x}=0.04}$

$\textsf{Taking log to both sides}\bold{:}$

$\quad \mathsf{log\big( x^{1-log_{5}x}\big)=log(0.04)}$

$\mathsf{Using\:log(a^{b})=b\:log(a)}\bold{:}$

$\to \mathsf{(1-log_{5}x)\:log(x)=log(0.04)}$

$\mathsf{We\:know\:that\:log_{a}(b)=\frac{log(a)}{log(b)}}\bold{:}$

$\quad \mathsf{\big(1-\frac{log(x)}{log(5)}\big)\:log(x)=log\big(\frac{1}{25}\big)}$

$\to \mathsf{log(x)-\frac{\{log(x)\}^{2}}{log(5)}=log(1)-log(25)}$

$\mathsf{Here,\:log(1)=0\:\&\:log(25)=2\:log(5)}\bold{:}$

$\quad \mathsf{log(5)\:log(x)-\{log(x)\}^{2}=-2\:\{log(5)\}^{2}}$

$\to \mathsf{\{log(x)\}^{2}-log(5)\:log(x)-2\:\{log(5)\}^{2}}$

$\textsf{Factorising, we get}\bold{:}$

$\quad \mathsf{\{log(x)-2\:log(5)\}\:\{log(x)+log(5)\}=0}$

$\therefore \mathsf{either\:log(x)-2\:log(5)=0}$

$\quad \mathsf{or,\:log(x)+log(5)=0}$

$\implies \mathsf{log(x)=log(5^{2}=log(25)}$

$\mathsf{\quad or,\:log(x)=log(\frac{1}{5})}$

$\implies \boxed{\mathsf{x=25,\:\frac{1}{5}}}$

$\textsf{The correct statement is option (a).}$

$\underline{\textsf{More questions related to logarithms}}\bold{:}$

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Answer 2

Answer:

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Step-by-step explanation:

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