Check the solution to "xlog4 m+1/2 log 4 n-log4 p"

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2022-04-25

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

nick1337

Expert2022-07-19Added 777 answers

$x \log (4 m) + \frac{1}{2} \log (4 n) - \log (4 p)$

Simplify each term.

Simplify $\frac{1}{2} \log (4 n)$ by moving $\frac{1}{2}$ inside the logarithm.

$x \log (4 m) + \log ({(4 n)}^{\frac{1}{2}}) - \log (4 p)$

Apply the product rule to $4 n$ .

$x \log (4 m) + \log (4^{\frac{1}{2}} n^{\frac{1}{2}}) - \log (4 p)$

Rewrite $4$ as $2^{2}$ .

$x \log (4 m) + \log ({(2^{2})}^{\frac{1}{2}} n^{\frac{1}{2}}) - \log (4 p)$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x \log (4 m) + \log (2^{2 (\frac{1}{2})} n^{\frac{1}{2}}) - \log (4 p)$

Cancel the common factor of $2$ .

$x \log (4 m) + \log (2^{1} n^{\frac{1}{2}}) - \log (4 p)$

Evaluate the exponent.

$x \log (4 m) + \log (2 n^{\frac{1}{2}}) - \log (4 p)$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$x \log (4 m) + \log (\frac{2 n^{\frac{1}{2}}}{4 p})$

Simplify each term.

Factor $2$ out of $2 n^{\frac{1}{2}}$ .

$x \log (4 m) + \log (\frac{2 (n^{\frac{1}{2}})}{4 p})$

Cancel the common factors.

$x \log (4 m) + \log (\frac{n^{\frac{1}{2}}}{2 p})$

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