Math Problem Statement

Write the following equation in its equivalent exponential form: log_5 25 = y

Solution

To convert the logarithmic equation log525=y\log_5 25 = y into its equivalent exponential form, we use the basic definition of logarithms:

logba=cis equivalent tobc=a.\log_b a = c \quad \text{is equivalent to} \quad b^c = a.

In your case:

  • The base b=5b = 5,
  • The result c=yc = y,
  • The number a=25a = 25.

Thus, the equivalent exponential form is:

5y=25.5^y = 25.

Let me know if you'd like further details or have any questions!

Here are five related questions to expand on this:

  1. What is the exponential form of log28=x\log_2 8 = x?
  2. How do you express log101000=z\log_{10} 1000 = z in exponential form?
  3. Can you solve for yy in the equation 5y=255^y = 25?
  4. What is the general relationship between logarithms and exponents?
  5. How would you rewrite logb1=0\log_b 1 = 0 in exponential form?

Tip: When converting between logarithmic and exponential forms, remember that the base of the logarithm becomes the base of the exponent.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponents

Formulas

log_b a = c is equivalent to b^c = a

Theorems

Basic properties of logarithms and exponents

Suitable Grade Level

Grades 8-10