Express as a single log and simplify: logb ^5-2lobb square root of x

Algebra
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Express as a single log and simplify:  logb ^5-2logb square root of x

Jun 14th, 2015

Thank you for the opportunity to help you with your question!

First we bring all numbers outside the logs to exponent position and simplify

logb^5 - log(bx^1/2)^2 = logb^5 - logb^2x

Then we apply the rule of logs which states that the difference of two logs can be expressed as the quotient of ONE log:

log(b^5/b^2x)

Now simplify

log(b^3/x)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 14th, 2015

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