6. Exponential & Logarithmic Functions

Solve each equation. 2|ln x|−6=0

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. log A = log B - C log x, for A

Solve each equation. 3|log x|−6=0

Solve each equation. $3^{x^2} = 45$

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. A = P (1 + r/n)^tn, for t

Solve each equation. ln(2x+1)+ln(x−3)−2 ln x=0

Solve each equation. ln 3−ln(x+5)−ln x=0

Solve each equation. $5^{x^2 - 12} = 25^{2x}$

To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^tn and A = Pe^rt Find t, to the nearest hundredth of a year, if \$1786 becomes \$2063 at 2.6%, with interest compounded monthly.

To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^tn and A = Pe^rt At what interest rate, to the nearest hundredth of a percent, will \$16,000 grow to \$20,000 if invested for 7.25 yr and interest is compounded quarterly?

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = 5^x, g(x) = log￬5 x

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬2 x+1, g(x) = 2^x-1

Use the properties of inverses to determine whether ƒ and g are inverses. ƒ(x) = log￬4 (x+3), g(x) = 4^x + 3

Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 3^x

Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^x-5