Math Problem Statement

The statement y = log_5 x is equivalent to ...

Solution

The question asks for an equivalent statement to y=log5xy = \log_5 x.

To convert a logarithmic equation into its exponential form, we can use the definition of logarithms:

y=logbxmeansby=xy = \log_b x \quad \text{means} \quad b^y = x

For y=log5xy = \log_5 x, this means:

5y=x5^y = x

So, the correct equivalent statement is:

x=5yx = 5^y

This corresponds to the last option in the list: x=5yx = 5^y.

Would you like further details or explanations?

Here are some related questions you might want to explore:

  1. What is the inverse of an exponential function?
  2. How do you convert an equation from logarithmic form to exponential form?
  3. What are the properties of logarithms?
  4. How does the base of a logarithm affect the solution?
  5. How do logarithmic and exponential functions relate to real-world problems?

Tip: Always remember that the logarithmic function y=logbxy = \log_b x is the inverse of the exponential function x=byx = b^y.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

y = log_b x is equivalent to b^y = x

Theorems

Logarithmic and Exponential Functions Relationship

Suitable Grade Level

Grades 9-12