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Solve log _{ 5 } 40 = y and check the solution.

Simplify.

log _{ 14 } 36

Evaluate the logarithm using the change of base formula.

log _{ 6 } 320

Check if x = e ^{ 9 } is a solution of the equation:

ln x = 9

Check if x = ln 2 is a solution of the equation:

4 e ^{ x } = 8

Solve the equation.

5 ^{ x } = 625

Solve for x .

8 e ^{ –x } = 4

Solve:

3 ^{ x } = 10

7 ^{ x } = 35

5 ^{ x } – 6 = 4

Solve for x :

4(2) ^{ 3 x } – 3 = 12

7 ^{ x } = 3 ^{ x }

10 ^{ x } ^{ – 4 } = 100 ^{ 3 x – 7 }

2 ^{ 5 x– 2 } = 5 ^{ 2 x+ 1 }

Solve the equation. Check your solution.

22 ^{ x } ^{ + 2 } = 57

ln x = 5

Solve 3 log _{ 2 } x = 15.

And check for extraneous solutions.

log _{ 10 } 3 x = 1.5

Solve the logarithmic equation.

3 log 2 x = –2

log x – log 4 = 4

2 log x – log 5 + log 3.2 = 12

Solve ln (5 x + 1) = ln (3 x + 7).

Solve ln x + ln ( x – 1) = 1, and check for extraneous solutions.

Solve ln _{ 6 } (13 – 5 x ) = ln _{ 6 } (1 – x ).

In order to double the investment in 5 years, at what rate of compound interest should the money be invested? Solve using common logarithms.

Consider the following model, N = N _{ 0 } e ^{ 2 t } , where N _{ 0 } is the initial number of particular species in a region and t is the time taken in years. How long will it take to triple in size?

Lauren deposited $ 800 in a bank that gives an annual interest of 6%. How long will it take for the deposit to reach $1500, if compounded continuously?

Use the formula for continuous compounding : A = Pe ^{ rt } ^{ }