If \log_5 x = 3, what is the value of x? — ACT

If $\log_5 x = 3$ , what is the value of $x$ ?

125

To solve the logarithmic equation

\log_5 x = 3

, we apply the fundamental definition of a logarithm. A logarithmic equation of the form

\log_b x = y

can be rewritten in exponential form as

b^y = x

. In this equation, the base

b

is 5 and the exponent

y

is 3. Rewriting gives

5^3 = x

. Evaluating

5^3

yields

5 \times 5 \times 5 = 125

. Therefore, the correct value of

x

is 125.

Apply the definition of a logarithm to rewrite the logarithmic equation in its equivalent exponential form.

5^3 = x

By definition,

\log_b x = y

is equivalent to

b^y = x

, where

b

is the base,

y

is the exponent, and

x

is the argument.

Evaluate the exponential expression

5^3

to solve for

x

x = 125

Cubing 5 means multiplying it by itself three times:

5 \times 5 \times 5 = 125

Definition of Logarithms

Question