Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic
expressions. Give the exact answer.
-$\log _ { 8 } x + \log _ { 8 } ( x - 63 ) = 2$
A) $\{ 64 \}$
B) $\{ 8 \}$
C) $\{ 1 , - 64 \}$
D) $\{ - 1,64 \}$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be combined into a single logarithm: $\log_8(x(x - 63)) = 2$. Converting to exponential form gives $8^2 = x(x - 63)$, simplifying to $x^2 - 63x - 64 = 0$. Factoring or using the quadratic formula yields $x = 64$ as the only solution within the domain (x > 63).

Solve the Logarithmic Equation log⁡8x+log⁡8(x−63)=2\log _ { 8 } x + \log _ { 8 } ( x - 63 ) = 2log8​x+log8​(x−63)=2

Solve the Logarithmic Equation $\log _ { 8 } x + \log _ { 8 } ( x - 63 ) = 2$