High School

Find the value of x, by converting to the exponential form and evaluating. Show all steps.




log5=6

Answer :

The value of x, given the equation log5 = 6, is 15625.

To find the value of x given the logarithmic equation log5 = 6, we need to convert it to exponential form and evaluate it. The exponential form of a logarithmic equation is expressed as:

x = b^y

where x is the base, b is the logarithm's base, and y is the value of the logarithm.

In this case, the base of the logarithm is 5 and the value of the logarithm is 6. In light of this, the equation can be rewritten as follows:

5^6 = x

Now, let's evaluate the expression:

5^6 = 5 × 5 × 5 × 5 × 5 × 5

= 25 × 25 × 25

= 625 × 25

= 15625

Therefore, the value of x, given the equation log5 = 6, is 15625.

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