Question

Find the exact solution, using common logarithms, and a two-decimal-place approximation of each solution.

log(7x + 4) = 2 + log(2x − 3)

Solve the equation.

log(x^3) = (log x)^2

Answer 1

log(7x + 4) = 2 + log(2x − 3)
log(7x + 4) - log(2x − 3) = 2
log( (7x+4)/(2x-3) ) = 2
(7x+4)/(2x-3) = 10^2 = 100
200x - 300 = 7x+4
193x = 304
x = 304/193 or appr 1.575

for the 2nd

log x^3 = log x^2
x^3 = x^2
x^3 - x^2 = 0
x^2(x-1) = 0
x = 0 or x = 1

but from log(2x-3) , 2x-3 > 0
2x > 3
x > 3/2

so there is not solution.