Evaluate log base 5 of 625

Problem

(log_5)(625)

Solution

1. Identify the definition of a logarithm, which states that (log_b)(x)=y is equivalent to by=x

2. Set up the equation by setting the expression equal to an unknown variable y

(log_5)(625)=y

3. Rewrite the logarithmic equation in its equivalent exponential form.

5=625

4. Express the number 625 as a power of the base 5 by calculating its factors.

625=5⋅5⋅5⋅5

625=5

5. Substitute the power back into the exponential equation.

5=5

6. Solve for y by equating the exponents since the bases are the same.

y=4

Final Answer

(log_5)(625)=4

Want more problems? Check here!