Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-ln (5 x-2)=ln 12-ln (x-6)
A) $\frac { 32 } { 5 }$
B) 0,$\frac { 32 } { 5 }$
C) 6 ,$\frac { 6 } { 5 }$
D) no solution

Question

Quizplus · Accepted Answer

To solve ln(5x-2) = ln 12 - ln(x-6), we use the property ln(a) - ln(b) = ln(a/b). This gives ln((5x-2)/(x-6)) = ln(12). Equating the arguments, we have (5x-2)/(x-6) = 12. Solving for x gives x = 32/5.

Use a Change of Base Formula to Evaluate the Given 325\frac { 32 } { 5 }532​

Use a Change of Base Formula to Evaluate the Given $\frac { 32 } { 5 }$