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

Question

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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