Solve the equation log7(3v+10)=0

Question

.(1 point)
v=

Answer 1

To solve the equation \( \log_7(3v + 10) = 0 \), we start by recalling that the logarithm of a number to a certain base is equal to zero when that number is equal to 1. This is based on the property:

\[ \log_b(a) = 0 \implies a = 1 \]

In our case:

\[ 3v + 10 = 1 \]

Now we can solve for \( v \):

1. Subtract 10 from both sides:

\[ 3v = 1 - 10 \] \[ 3v = -9 \]

2. Now divide by 3:

\[ v = \frac{-9}{3} \] \[ v = -3 \]

Therefore, the solution is:

\[ v = -3 \]