Solve the equation.
-$$\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$$
A) $\varnothing$
B) $\{ 3 \}$
C) $\{ 3,0 \}$
D) $\{ 9 \}$

Question

Quizplus · Accepted Answer

To solve the equation $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$, we first recognize that $8 = 2^3$, which allows us to rewrite the equation in a common base. The equation becomes $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \frac { 1 } { 3 } \log _ { 2 } ( 3 x )$. Since the coefficients and bases on both sides are the same, we can equate the arguments: $x + 6 = 3x$. Solving for $x$ gives $x = 3$, which is the only solution.

Solve the Equation 13log⁡2(x+6)=log⁡8(3x)\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )31​log2​(x+6)=log8​(3x)

Solve the Equation $\frac { 1 } { 3 } \log _ { 2 } ( x + 6 ) = \log _ { 8 } ( 3 x )$