Posted by **Eric** on Wednesday, April 24, 2013 at 4:09pm.

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

- Math -
**Reiny**, Wednesday, April 24, 2013 at 6:14pm
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.

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