Logarithm Question (Find x) How to solve x for x^(2 log_(10)x)=(x^5)/(100)?

Elliana Molina

Elliana Molina

Answered question

2022-11-08

Logarithm Question (Find x)
How to solve x for
x 2 log 10 x = x 5 100 ?

Answer & Explanation

brulotfao

brulotfao

Beginner2022-11-09Added 16 answers

I'll write log for log 10 . Take the log of both sides. You get
2 log ( x ) 2 = 5 log ( x ) 2.
Now let y = log ( x ). You have a quadratic equation
2 y 2 5 y + 2 = 0
which you can factor as
( 2 y 1 ) ( y 2 ) = 0.
So y = 2 or y = 1 / 2, so x = 100 or x = 10
perlejatyh8

perlejatyh8

Beginner2022-11-10Added 4 answers

Starting with
x 2 log 10 x = x 5 100
Take l o g x of both sides of the equation.
Notice that: l o g x 10 = 1 l o g 10 x ; and now solve!

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