Question

Rewrite the following equation in logarithmic form and exponential form

Answer 1

- The logarithmic form of
`\( 0.25 = 2^(-2) \)` is
`\( \log_2(0.25) = -2 \).`

- The exponential form of
`\( \log_8(512) = 3 \)` is
`\( 8^3 = 512 \).`

To rewrite the exponential equation
`\( 0.25 = 2^(-2) \)` in logarithmic form, you use the definition of a logarithm. The logarithmic form of
`\( a^b = c \)` is
`\( \log_a(c) = b \)`. Applying this to the given equation:

`\[ 2^(-2) = 0.25 \]`

`\[ \log_2(0.25) = -2 \]`

This is the logarithmic form of the equation.

To rewrite the logarithmic equation
`\( \log_8(512) = 3 \)` in exponential form, you use the definition of a logarithm in reverse. The exponential form of
`\( \log_a(c) = b \) is \( a^b = c \)`. Applying this to the given equation:

`\[ \log_8(512) = 3 \]`

`\[ 8^3 = 512 \]`

This is the exponential form of the equation.

So, summarizing the results:

- The logarithmic form of
`\( 0.25 = 2^(-2) \)` is
`\( \log_2(0.25) = -2 \).`

- The exponential form of
`\( \log_8(512) = 3 \)` is
`\( 8^3 = 512 \).`

Answer 2

Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Explanation: