Math, asked by ashutoshkoirala, 4 months ago

If 5= 0.04, Find the value of x

Answers

Answered by mrjoker07
5

I think the question is wrong ......

so could you please read the question.......

if 5x = 0.04 is the question

then x = 0.008 is the ANSWER......

Answered by Abhisheksingh5722
7

We have to find the value of x here

:

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

1−log

5

x

=0.04

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

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

1−log

5

x

)=log(0.04)

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

b

)=blog(a):

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

5

x)log(x)=log(0.04)

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

a

(b)=

log(b)

log(a)

:

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

log(5)

log(x)

)log(x)=log(

25

1

)

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

log(5)

{log(x)}

2

=log(1)−log(25)

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

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

2

=−2{log(5)}

2

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

2

−log(5)log(x)−2{log(5)}

2

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

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

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

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

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

2

=log(25)

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

5

1

)

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

x=25,

5

1

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

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

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