Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$
A) $\sqrt { 26 }$
B) $- \sqrt { 26 } , \sqrt { 26 }$
C) -7,7
D) 7

Question

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places.
-$\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$
A) $\sqrt { 26 }$
B) $- \sqrt { 26 } , \sqrt { 26 }$
C)  -7,7 
D) 7

Quizplus · Accepted Answer

The equation simplifies to $2 \log_4(x-5) = 1$, which means $\log_4(x-5) = 0.5$. Converting to exponential form gives $x-5 = 4^{0.5} = 2$, so $x = 7$.

Use a Change of Base Formula to Evaluate the Given log⁡4(x−5)+log⁡4(x−5)=1\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1log4​(x−5)+log4​(x−5)=1

Use a Change of Base Formula to Evaluate the Given $\log _ { 4 } ( x - 5 ) + \log _ { 4 } ( x - 5 ) = 1$