Question
Solve: log base 7 (3v + 10) = 0
Answers
GPT-4o mini
To solve the equation \( \log_7(3v + 10) = 0 \), we can use the property of logarithms that states \( \log_b(x) = 0 \) implies that \( x = 1 \) when \( b > 1 \).
Applying this property here, we set the argument of the logarithm equal to 1:
\[
3v + 10 = 1
\]
Next, we solve for \( v \):
\[
3v = 1 - 10
\]
\[
3v = -9
\]
\[
v = \frac{-9}{3}
\]
\[
v = -3
\]
Thus, the solution is
\[
\boxed{-3}
\]
Applying this property here, we set the argument of the logarithm equal to 1:
\[
3v + 10 = 1
\]
Next, we solve for \( v \):
\[
3v = 1 - 10
\]
\[
3v = -9
\]
\[
v = \frac{-9}{3}
\]
\[
v = -3
\]
Thus, the solution is
\[
\boxed{-3}
\]