6. Exponential & Logarithmic Functions

In Exercises 93–102, solve each equation. 3^x+2 ⋅ 3^x=81

In Exercises 93–102, solve each equation. 2|ln x|−6=0

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. log A = log B - C log x, for A

In Exercises 93–102, solve each equation. 3|log x|−6=0

In Exercises 93–102, solve each equation. 3^x2=45

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. A = P (1 + r/n)^(tn), for t

In Exercises 93–102, solve each equation. ln(2x+1)+ln(x−3)−2 ln x=0

In Exercises 93–102, solve each equation. ln 3−ln(x+5)−ln x=0

In Exercises 93–102, 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