Solve the equation. log 10 ( 2 x $-$ 27 ) $-$ log 10 ( x $-$ 4 ) = 1
A) $x = \frac { 17 } { 8 }$
B) $x = \frac { 13 } { 8 }$
C) $x = \frac { 11 } { 8 }$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, we have:
log 10 (2x - 27) - log 10 (x - 4) = 1
log 10 [(2x - 27)/(x - 4)] = 1
(2x - 27)/(x - 4) = 10^1
2x - 27 = 10(x - 4)
2x - 27 = 10x - 40
8x = 13
x = 13/8

So, the answer is B.

Solve the Equation −-− 27 ) −-− Log 10 ( X −-− 4 ) = 1 A)

Solve the Equation $-$ 27 ) $-$ Log 10 ( X $-$ 4 ) = 1
A)