Question

Given that x=lg a is a solution of the equation 10^(2x+1)-7(10^x) =26. Find the value of a.

Answer 1

10 *(10^x)^2 - 7 (10^x) = 26

let z = 10^x

10 z^2 - 7 z -26 = 0

( z - 2)( 10 z + 13) = 0

10^x = 2 or 10^x = -1.3

if you log is base 10

log 10^x = x = log 2

but if x = log a
then log a = log 2
so a = 2

similarly
log 10^x = x = log (-1.3) but not allowed :)