Exponential Functions Exercises

Example 1

Evaluate y = 3^x + 2^{(x – 4)} – 2^{(x – 2)} when x = 4 without using a calculator.

Hint

Solve each term individually.

Example 2

Evaluate y = 100^0.75x(10^{1.5x – 3}) when x = 2 without using a calculator.

Hint

Find a common base and combine first.

Example 3

Solve for x:

e^x = e^{(2x + 4)}

Hint

If you take the natural log of both sides, you can drop those bases.

Example 4

Solve for x:

3^{(3x + 1)} = 9^x

Hint

Find a common base first.

Example 5

Solve for x:

256 = 4²^x

Hint

Try rewriting it as 4⁴ = 4^2x.

Example 6

Solve for x and round your answer to three decimal places:

9^-5x(9^17x) = 81

Hint

We can combine those exponents on the right to get 9^{(-5x + 17x)} = 81, then simplify and find a common base.

Example 7

Solve for x:

150(2)^2x = 300

Hint

Divide both sides by 150 first.

Example 8

Solve for x:

Hint

Change the right side to 8^-4x, then find a common base on both sides.

Example 9

Solve for x:

e^4x = e^{(9x – 4)}

Hint

Use the natural log.

Example 10

Solve for y:

10^xy = 100^{(4xy – 2)}

Hint

Find a common base first.

Exponential Functions Exercises

Exponential Functions Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

Example 8

Example 9

Example 10

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