Solve the equation. Do not use a calculator. $$\log _ { 6 } 8 x = \log _ { 6 } 48$$
A) $x = 48$
B) $x = 6$
C) $x = 1$
D) $x = 8$
E) $x = 7$

Question

Quizplus · Accepted Answer

Using the fact that $$\log _ { b } ( b ^ { n } ) = n$$, we can simplify the equation as follows: $$\log _ { 6 } 8 x = \log _ { 6 } 48 \Rightarrow \log _ { 6 } (8x/48) = \log _ { 6 } (1/6)$$

Now use the definition of logarithm  $\log _ { b } c=\iff b^{d} = c$ with base 6 
$$6^{\log _ { 6 } (8x/48)} = 6^{\log _ { 6 } (1/6)} \Rightarrow 8x/48 = 1/6$$

Solving the above equation, we get $x=6$. Therefore, the answer is B)  $x = 6$.

Solve the Equation log⁡68x=log⁡648\log _ { 6 } 8 x = \log _ { 6 } 48log6​8x=log6​48

Solve the Equation $\log _ { 6 } 8 x = \log _ { 6 } 48$