xlog4 m+1/2 log 4 n-log4 p

2022-04-25 Answered

xlog4 m+1/2 log 4 n-log4 p

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Answers (1)

nick1337
Answered 2022-07-19 Author has 564 answers

xlog(4m)+12log(4n)-log(4p)

Simplify each term.

Simplify 12log(4n) by moving 12 inside the logarithm.

xlog(4m)+log((4n)12)-log(4p)

Apply the product rule to 4n.

xlog(4m)+log(412n12)-log(4p)

Rewrite 4 as 22.

xlog(4m)+log((22)12n12)-log(4p)

Apply the power rule and multiply exponents, (am)n=amn.

xlog(4m)+log(22(12)n12)-log(4p)

Cancel the common factor of 2.

xlog(4m)+log(21n12)-log(4p)

Evaluate the exponent.

xlog(4m)+log(2n12)-log(4p)

Use the quotient property of logarithms, logb(x)-logb(y)=logb(xy).

xlog(4m)+log(2n124p)

Simplify each term.

Factor 2 out of 2n12.

xlog(4m)+log(2(n12)4p)

Cancel the common factors.

xlog(4m)+log(n122p)

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