Question

Help with exponential equations, please!

Answer 1

Angie was working on solving the exponential equation 23^x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation and how solving would be different if the bases were equal.

Answer 2

I understand how to solve the provided equation. But how would it be different if the bases were equal?

Answer 3

@jim_thompson5910 @Jhannybean @mathstudent55 @Nnesha

Answer 4

the base is 23? or is it 2*3? or 2^3 ?

Answer 5

\[23^x=6\]

Answer 6

example
\[\huge\rm log_b x = y \]
\[\huge\rm b^y = x\]
change taht exponential to log form

Answer 7

apply logs to both sides to pull down the exponent

\[\Large 23^x = 6\]
\[\Large \log(23^x) = \log(6)\]
\[\Large x\log(23) = \log(6)\]
\[\Large x = \frac{\log(6)}{\log(23)}\]
\[\Large x = \log_{23}(6)\]

On step 3, I'm using the rule log(x^y) = y*log(x). This property is the primary reason why logs are used to solve exponential equations. Logs undo exponentials. On the last step I'm using the change of base formula

Answer 8

Thank you once again!!