Evaluate log base 25 of 5

Problem

(log_25)(5)

Solution

1. Identify the logarithmic expression as an equation where x is the value we want to find.

(log_25)(5)=x

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

25=5

3. Express the base 25 as a power of 5 to create a common base on both sides of the equation.

(5)x=5

4. Apply the power of a power rule (am)n=a(m*n) to simplify the left side.

5(2*x)=5

5. Equate the exponents since the bases are now identical.

2*x=1

6. Solve for x by dividing both sides by 2

x=1/2

Final Answer

(log_25)(5)=1/2

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