Rewrite As An Exponential Equation.

How tin can your rewrite a logarithm expression?

Earlier yous try to understand the formula for how to rewrite a logarithm equation every bit exponential equation, you should be comfortable solving exponential equations

As the examples beneath volition show yous, a logarithmic expression similar $$ log_2 256 $$ is just a different way of writing an exponent!

Examples

Example one

Evaluate: $$ log_5 25 $$

Example ii

Evaluate: $$ log_4 64 $$

Example 3

Evaluate: $$ log_4 16 $$

Case 4

Evaluate: $$ log_4 216 $$

Practice Bug

Trouble 1

Evaluate $$ log_4 8 $$

Step 2

Bottom, base. End exponent:

Step iii

$$ 4^10 = eight \\ four^{\frac{three}{two}} =8 \\ x =\frac{3}{two} $$

Problem ii

Evaluate $$ log_8 sixteen $$

Pace 2

Bottom, base. Stop exponent:

Stride 3

$$ 8^x = 16 \\ 8^{\frac{iv}{3}} = 16 \\ x =\frac{iv}{3} $$

Problem 3

Evaluate $$ log_{25} 125$$

Step 2

Bottom, base. End exponent:

Pace 3

$$ 25^x = 125 \\ 25^{\frac{3}{ii}} = 125 \\ ten =\frac{3}{2} $$

Problem 4

Evaluate $$ log_{145} i$$

Stride 2

Bottom, base. End exponent:

Step iii

$$ 145^x = 1 \\ 10 =0 $$

Call back any number raised to an exponent of 0, zero, is one.

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