Question

How do you solve exponential equations that have different bases, such as 6^x-1 = 4.5^ 3x-1

Answer 1

Hint :take log to both sides to get the power down .

Answer 2

Assuming \[6^{x-1}=4.5^{3x-1}\]

You have to use logs.

log both sides:
\[\log(6^{x-1})=\log(4.5^{3x-1})\]

Use the power rule to move the exponents as coefficients.
\[(x-1)\log(6)=(3x-1)\log(4.5)\]

Now distribute the coefficients to both sides, combine like terms, and move x's to one side. Then you can factor out the x and divide for the answer.

Answer 3

Thank you for your insight! I just completely drew a blank on this one.