If 5= 0.04, Find the value of x
Answers
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......
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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