Write the equation in exponential form, solve for x

Question

log₇(2x + 17) = 2

Answer 1

Use the definition of logarithm:

log_b(x) = c is the same thing as x = b^c:

2x +17 = 7²

Now solve for x:

2x +17 = 49

2x = 49 - 17 = 32

x = 32 / 2 = 16

Check:

log₇(2x + 17) = log₇(2(16) + 17) = log₇(32 + 17) = log₇(49) = log₇(7²) = 2*log₇(7) = 2*1 = 2.

Answer 2

Hello Allie!

We have:

log₇(2x + 17) = 2

Which is the same as

2x + 17 = 7²

2x + 17 = 49

2x = 32

x = 16

Feel free to message with doubts! Best regards!