Math Problem Statement

Translate the logarithmic statement into an equivalent exponential statement.

log Subscript 4 Baseline 256log4256equals=44

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Part 1

The equivalent exponential equation is

enter your response here.

​(Use integers or decimals for any numbers in the​ equation.)

Solution

To translate the logarithmic statement into an equivalent exponential statement, let's first break down the given logarithmic expression:

log4256=4\log_4 256 = 4

This means that the logarithm of 256 with base 4 equals 4. In exponential form, this statement is rewritten as:

44=2564^4 = 256

So, the equivalent exponential equation is:

44=2564^4 = 256

Would you like further clarification or details on logarithms and exponents?

Here are 5 related questions to expand on this concept:

  1. What is the general form for converting a logarithmic expression into exponential form?
  2. How do you evaluate logarithms without a calculator?
  3. What is the logarithm of a number when the base equals the number itself?
  4. How can you express log264=6\log_2 64 = 6 in exponential form?
  5. What are the properties of logarithms that make them useful in solving equations?

Tip: To check if you have the correct logarithmic or exponential form, always remember that logbx=y\log_b x = y means by=xb^y = x.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Exponential Functions

Formulas

log_b(x) = y ↔ b^y = x

Theorems

Exponential-Logarithmic Relationship

Suitable Grade Level

Grades 8-10