6. Exponential & Logarithmic Functions

Solve each equation. Give solutions in exact form. See Examples 5–9. log_5 [(3x + 5)(x + 1)] = 1

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. log3(x+4)=−3

Solve each equation. Give solutions in exact form. See Examples 5–9. log(x + 25) = log(x + 10) + log 4

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. log4(3x+2)=3

Solve each equation. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (ln x)(ln 1) = 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. 5 ln(2x)=20

In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x

Solve each equation. Give solutions in exact form. See Examples 5–9. ln(7 - x) + ln(1 - x) = ln (25 - x)

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. 6+2 ln x=5

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2^(4x-2) = 64

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+3=1

Solve each equation. Give solutions in exact form. See Examples 5–9. log_8 (x + 2) + log_8 (x + 4) = log_8 8

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x = 7000

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. log5 x+log5(4x−1)=1