91Ó°ÊÓ

Evaluate each expression. Do not use a calculator.

${\log }_2\left(\frac{1}{8}\right)$

Solve the following equation for 'x'.

${\log }_2\left(x-4\right)+{\log }_2\left(x+4\right)=3$

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

$\log \left(2x+1\right)=1+\log \left(x−2\right)$

Approximate each number using a calculator. Express your answer rounded to three decimal places.

(a)$3.1^{2.7}$

(b) $3.{14}^{2.71}$

(c) $3.{141}^{2.718}$

(d)${\mathrm{Ï€}}^{\mathrm{e}}$

Find the principal needed now to get each amount; that is, find the present value to get $600 after 2 years at 4% compounded quarterly.

Find$f\left(3x\right)$if$f\left(x\right)=4-2x^2$.

Solve the inequality :$\frac{x-1}{x+4}>0$

Where is the function $f\left(x\right)=x^2$increasing? Where is it decreasing?

${\log }_{a}a$

Solve the inequality$\frac{x-1}{x+4}>0$.