Question

Write the quantity using sums and differences of simpler logarithmic expressions.

a. log10(square root (x + 6)(x + 7))

b. ln (squared root(x + 6)(x + 7) divided by
(squared root(x − 6)(x − 7)

Answer 1

\[\ln(\frac{\sqrt{(x+6)(x+7)}}{\sqrt{(x-6)(x-7)}})=\ln(\sqrt{(x+6)(x+7)})-\ln(\sqrt{(x-6)(x-7)})\]
\[=\ln[(x+6)(x+7)]^\frac{1}{2}-\ln[(x-6)(x-7)]^\frac{1}{2}\]
\[=\frac{1}{2}*\ln[(x+6)(x+7)]-\frac{1}{2}*\ln[(x-6)(x-7)]\]
\[=\frac{1}{2}*[\ln(x+6)+\ln(x+7)]-\frac{1}{2}*[\ln(x-6)+\ln(x-7)]\]

Answer 2

is b

Answer 3

\[\log_{10}\sqrt{(x+6)(x+7)}=\log(((x+6)(x+7))^{1/2})\]\[=1/2*(\log((x+6)(x+7))\]\[=1/2*[\log(x+6)+\log(x+7)]\]