Solve for x log base 5 of 25=x

Problem

(log_5)(25)=x

Solution

1. Identify the logarithmic equation in the form (log_b)(a)=x where the base b=5 and the argument a=25

2. Rewrite the equation in its equivalent exponential form using the definition (log_b)(a)=x⇔bx=a

5=25

3. Express the number 25 as a power of the base 5.

25=5

4. Substitute the power back into the exponential equation.

5=5

5. Equate the exponents since the bases are the same.

x=2

.

Final Answer

(log_5)(25)=2

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