6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. ln e^x - 2 ln e = ln e⁴

Solve the logarithmic equation.

$\(\log\)_3\(\left\)(3x+9\(\right\))=\(\log\)_35+\(\log\)_312$

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5^x=125

Solve each equation. Give solutions in exact form. log x² = (log x)²

Find ƒ^-1(x), and give the domain and range. ƒ(x) = e^x + 10

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?

Solve each equation. Give solutions in exact form. ln 4x = 1.5

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. e^2x−3e^x+2=0

Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log(3x−3)=log(x+1)+log 4

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 5(1.015)^x-1980 = 8

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 3^1-x=1/27

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

Solve each equation. Give solutions in exact form. log₅ [(3x + 5)(x + 1)] = 1

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. $e^{x^2}=100$

Find the error in the following 'proof' that 2 < 1.