# How do you condense Log2r-2log4p+1/2log16x+2?

Jul 26, 2016

#### Answer:

$\log \left[\frac{50 r {x}^{\frac{1}{2}}}{p} ^ 2\right]$

#### Explanation:

Before we can condense all the terms, they all need to be log terms.
$L o g 2 r - 2 \log 4 p + \frac{1}{2} \log 16 x + 2$?
$2 = \log 100$
$L o g 2 r - 2 \log 4 p + \frac{1}{2} \log 16 x + \log 100$

Use the power law:

=$L o g 2 r - \log {\left(4 p\right)}^{2} + \log {\left(16 x\right)}^{\frac{1}{2}} + \log 100$

If logs are being added or subtracted, the numbers are being multiplied or divided.

= $\log \left[\frac{2 r \times {\left(16 x\right)}^{\frac{1}{2}} \times 100}{{\left(4 p\right)}^{2}}\right]$

=$\log \left[\frac{200 r \times 4 {\left(x\right)}^{\frac{1}{2}}}{16 {p}^{2}}\right]$

=$\log \left[\frac{50 r {x}^{\frac{1}{2}}}{p} ^ 2\right]$