Write an equivalent expression in exponential form.
-$$\log _ { 1 / 2 } ( x + 6 ) = - 7$$
A) 128
B) 140
C) 122
D) 134

Question

Quizplus · Accepted Answer

To convert the given logarithmic equation $\log _ { 1 / 2 } ( x + 6 ) = - 7$ to its exponential form, we use the definition of logarithms: if $\log_b a = c$, then $b^c = a$. Applying this to the given equation, we get $(1/2)^{-7} = x + 6$. Simplifying, $2^7 = x + 6$, which gives $128 = x + 6$. Solving for $x$, we find $x = 122$.

Write an Equivalent Expression in Exponential Form log⁡1/2(x+6)=−7\log _ { 1 / 2 } ( x + 6 ) = - 7log1/2​(x+6)=−7

Write an Equivalent Expression in Exponential Form $\log _ { 1 / 2 } ( x + 6 ) = - 7$