Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-ln x-ln (x-4)=ln 4
A) $\frac { 16 } { 3 }$
B) $\frac { 4 \ln 4 } { \ln 4 - 1 }$
C) 0
D) no solution

Question

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-ln x-ln (x-4)=ln 4 
A) $\frac { 16 } { 3 }$
B) $\frac { 4 \ln 4 } { \ln 4 - 1 }$
C) 0
D) no solution

Quizplus · Accepted Answer

Using the properties of logarithms, specifically the subtraction property which states $\ln a - \ln b = \ln(\frac{a}{b})$, we can rewrite the given equation as $\ln(\frac{x}{x-4}) = \ln 4$. Since the bases of the logarithms are the same, we can equate the arguments: $\frac{x}{x-4} = 4$. Solving for $x$ gives $x = \frac{16}{3}$.

Use a Change of Base Formula to Evaluate the Given 163\frac { 16 } { 3 }316​

Use a Change of Base Formula to Evaluate the Given $\frac { 16 } { 3 }$