Help with algebra please!!

Question

Erika is working on solving the exponential equation 50^x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation by using the change of base formula  

Answer 1

Hi Jessica,

50^X = 17

log 50^x = log 17

x * log 50 = log 17

x = log 17 / log 50

the magic of logs is that it frees up our exponent. you can take the exponent on the 50 and place it in front of the log 50. Then just divide out the log 50 : )

hope this helped. Cheers!

upon further inspection, it appears they might be asking for an alternate solution using change of base.

in that case…

log₅₀ ( 50^x) = log₅₀ (17)

place the x in front of the log,

x * log₅₀(50) = log₅₀(17)

recall that log₅₀(50) = 1

x = log₅₀(17)