Retaining the Concepts. Expand:

Question

\log_{7} (\frac{5 \sqrt{x}}{49 y^{10}})

Accepted Answer

hey everyone here we are asked to use the properties of logarithms. To expand the logarithmic expression log base four of the ninth root of X. All divided by 16 Y to the power of 13. Now our first expansion here can be done by recalling the the quotient rule which allows us to rewrite this expression as log base four of the ninth root of x minus log base four of 16 times Y to the power of 13. And our next expansion can be done to the sea second term here by recalling the product rule. So we can rewrite our expression as log base four of the ninth root of x minus Now the quantity of log base four of plus log base four of Y to the power of 13. And now we can make some simplifications by factoring in this negative sign and we can also clearly identify what powers we have. So doing this, we have log base four of instead of the ninth root of X. We can rewrite this as X to the power of 1/ and now we have minus log base four and instead of 16 we can rewrite it as four to the power of two minus log base four of y to the power of 13. And now from here with our powers clearly identified, we can x expand this further by recalling the power role, allowing us to bring out the powers as coefficients. So we now have 1/9 log, base four of x minus two times log base four of four minus 13 times log base four of Y. And next we need to note that log base four of four is equal to one, so this part of the term here is equal to one. So now we can rewrite the expression as our final expansion which is 1/9 times log base four of x minus two. Now because the coefficient two times one is just to minus 13 times log base four of Y. And with this we are done expanding and we are left with answer choice. C. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Retaining the Concepts. Expand: $\log_{7} (\frac{5 \sqrt{x}}{49 y^{10}})$

Key Concepts

Properties of Logarithms

Radicals and Exponents

Simplifying Algebraic Expressions Inside Logarithms

Watch next