Question

Write the logarithmic equation in exponential form. For example, the exponential form of log₅ 25 = 2 is 5² = 25. log₈ 1/512 = -3

a) 8⁻³=1/512
b) 8³=1/512
c) 8⁻³=512
d) 8³=512

Answer 1

logarithmic equation in exponential form is
`\(8^(-3) = (1)/(512)\)` (option a)

Step-by-step explanation:

To convert the logarithmic equation
`\( \log_8 (1)/(512) = -3 \)` into exponential form, we use the definition of logarithms. The logarithmic form
`\( \log_b x = y \)` can be expressed as
`\( b^y = x \).` (option a)

For the given equation
`\( \log_8 (1)/(512) = -3 \)`, this translates to
`\( 8^(-3) = (1)/(512) \)` The base (8) raised to the power of the logarithm (-3) equals the value inside the logarithm (1/512).

Therefore, the correct exponential form is
`\( 8^(-3) = (1)/(512) \)`, which corresponds to option (a).

Answer 2

The logarithmic equation log₈ 1/512 = -3 in exponential form is 8⁻³ = 1/512, showing the inverse nature of logarithms and exponents. So, the correct answer is a) 8⁻³=1/512.

Step-by-step explanation:

To write the logarithmic equation log₈ 1/512 = -3 in exponential form, we need to understand that the logarithm base 8 of 1/512 equals -3, which means that 8 raised to the power of -3 gives us 1/512.

Therefore, the exponential form of the given logarithmic equation is 8⁻³ = 1/512.

Remember, the relationship between logarithms and exponents is such that if logₙ x = y, then it can be written in exponential form as bʸy = x, where b is the base of the logarithm.

This reflects the inverse nature of logarithmic and exponential functions, where they essentially undo each other's operations.

Thus, the correct answer is a) 8⁻³=1/512.