Which logarithmic equation is equivalent to 82 = 64?

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lisboa lisboa · Answer 1 · 2018-12-26T07:33:12+01:00

Answer:

[tex]log_8(64) = 2[/tex]

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

[tex]b^x= a[/tex]

[tex]log_b(a) = x[/tex]

base of exponent becomes the base of log as well

[tex]8^2= 64[/tex] can be written as

[tex]log_8(64) = 2[/tex]

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psm22415 psm22415 · Answer 2 · 2022-02-01T09:30:34+01:00

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

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;

[tex]\rm b^x=a\\\\Taking \ log \ on \ both \ sides\\\\log_b(a)=x\\[/tex]

Substitute the values in the formula;

[tex]\rm log_b(a)=x\\\\ log_8(64) =2[/tex]

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

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

https://brainly.com/question/2657754