Which logarithmic equation is equivalent to 82 = 64?

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lisboa lisboa · Answer 1 · 2018-12-26T01:33:12-05:00

Answer:

\(log_8(64) = 2\)

Step-by-step explanation:

8^2 = 64

here base is 8 and exponent is 2

To change exponential form to log form we apply formula

\(b^x= a\)

\(log_b(a) = x\)

base of exponent becomes the base of log as well

\(8^2= 64\) can be written as

\(log_8(64) = 2\)

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psm22415 psm22415 · Answer 2 · 2022-02-01T03:30:34-05:00

The logarithmic equation is equivalent to the given equation is \(\rm log_8(64) =2\).

We have to determine

Which logarithmic equation is equivalent to 8^2 = 64?

The logarithm is an exponent or power to which a base must be raised to obtain a given number.

The logarithmic equation is equivalent to 8^2 = 64 is;

Here the base is 8 and the exponent is 2

To change exponential form to log form we apply the formula;

\(\rm b^x=a\\\\Taking \ log \ on \ both \ sides\\\\log_b(a)=x\\\)

Substitute the values in the formula;

\(\rm log_b(a)=x\\\\ log_8(64) =2\)

Hence, the logarithmic equation is equivalent to the given equation is \(\rm log_8(64) =2\).

To know more about the Logarithmic equation click the link given below.

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