Question

Solve the equation. Enter the answer as an improper fraction.

log7(−8b−10)=2
log
7
⁡
(
−
8
𝑏
−
10
)
=
2



(1 point)
b=
𝑏
=

Answer 1

To solve the equation

\[
\log_7(-8b - 10) = 2,
\]

we want to rewrite it in exponential form. Recall that the logarithmic equation

\[
\log_a(x) = y
\]

can be rewritten as

\[
x = a^y.
\]

Applying this to our equation, we have:

\[
-8b - 10 = 7^2.
\]

Calculating \(7^2\):

\[
7^2 = 49.
\]

Thus, we can rewrite the equation as:

\[
-8b - 10 = 49.
\]

Next, we will isolate \(b\). Start by adding 10 to both sides:

\[
-8b = 49 + 10,
\]
\[
-8b = 59.
\]

Next, divide both sides by -8:

\[
b = \frac{59}{-8},
\]
\[
b = -\frac{59}{8}.
\]

Therefore, the solution to the equation is:

\[
\boxed{-\frac{59}{8}}.
\]