SOLUTION: Please show the step-by-step solution to: Prove [(log7)4][log4)9]= [(log7)9] Textbook hint: start by dividing each side by [(log7)4]..... Thank you!

Question 170951This question is from textbook LOF Advanced Algebra
: Please show the step-by-step solution to:
Prove [(log7)4][log4)9]= [(log7)9]
Textbook hint: start by dividing each side by [(log7)4].....
Thank you! This question is from textbook LOF Advanced Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Here's one way to do it:

Start with the given equation. Note: I'm ONLY going to manipulate the left side. The right side is for comparison

By the change of base formula , we can rewrite into

Also, we can rewrite into

Use the change of base formula to expand the logarithms (see above)

Highlight the common terms.

Cancel out the common terms.

Simplify

Combine and multiply the fractions.

Use the change of base formula (in reverse) to simplify the left side

So this shows us that

Note: this can be generalized to say that

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