Math  /  Algebra

QuestionChange the logarithmic statement to an equivalent statement involving an exponent. log5625=4\log _{5} 625=4
The equivalent exponential statement is \square . (Type an equation.)

Studdy Solution

STEP 1

1. We are given a logarithmic equation and need to convert it to an exponential form.
2. The base of the logarithm is 5, the argument of the logarithm is 625, and the result is 4.

STEP 2

1. Understand the relationship between logarithms and exponents.
2. Convert the logarithmic statement to an exponential statement.

STEP 3

Recall the definition of a logarithm: If logba=c\log_b a = c, then the equivalent exponential form is bc=ab^c = a.
For the given logarithmic statement log5625=4\log_5 625 = 4, identify the components: - Base b=5b = 5 - Argument a=625a = 625 - Result c=4c = 4

STEP 4

Using the relationship between logarithms and exponents, convert the logarithmic statement to an exponential statement:
54=625 5^4 = 625
This is the equivalent exponential statement.
The equivalent exponential statement is:
54=625 \boxed{5^4 = 625}

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