Solve each equation. 3^x+2 ⋅ 3^x=81

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. ln(x−2)−ln(x+3)=ln(x−1)−ln(x+7)

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. y = K/(1+ae^-bx), for b

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. y = A + B(1 - e^-Cx), for x

Solve each equation. 5^2x ⋅ 5^4x=125

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. $3^{x^2} = 45$