Step 1 is convert all the logs to the same base. Use log base 10 because if you were doing this for a final calculation, you'd use log base 10. Most calculators have a log (base 10) button.

a/b/c = a*c/b

When there's a fraction in the denominator, flip it and multiply it by the numerator.

That manipulation gives

Remember that if then

Drop the denominator log(a)

Power rule is

Quotient rule is

and

Divide 8 and 16 by 8.

As the Fonz would say, "Checkamundo!"

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Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


I'm not sure what method you tried for base conversion, but considering your description of the result, you either used an incorrect method or made an algebra error in your process.

To convert from logarithm base to logarithm base use:



So, since you chose as your common base, do the conversions as above:



But since we know that:



We can derive that



Hence:



From which we get:



Similar analysis yields:



And then:



Can be written as:



Then multiply by the common denominator to get:



A true statement.

John

My calculator said it, I believe it, that settles it