I have to solve the equation by finding the exact solution. Please Help.

Question

1/4 log(x)-log(10000)=4

Answer 1

lgt ( x ) = The base 10 logaritam

lgt ( 10000 ) = 4

( 1/4 ) lgt (x) - lgt( 10000 ) = 4

( 1/4 ) lgt (x) - 4 = 4

( 1/4 ) lgt (x) = 4 + 4

( 1/4 ) lgt (x) = 8 Multiply both sides with 4

lgt ( x ) = 32

10 ^ lgt ( x ) = 10 ^ 32

Remark : 10 ^ lgt ( x ) = x

x = 10 ^ 32