Math Problem Statement

C 4^5 is not correct

Convert the exponential equations into logarithmic form.

Solution

The problem is about converting exponential equations into their logarithmic forms. Let's focus on the first part (a), which asks you to convert 45=10244^5 = 1024 into logarithmic form.

For exponential expressions of the form ab=ca^b = c, the corresponding logarithmic form is loga(c)=b\log_a(c) = b.

So for 45=10244^5 = 1024, the logarithmic form is: log4(1024)=5\log_4(1024) = 5

Therefore, C=1024C = 1024 and D=5D = 5.

It seems that in your question, CC is incorrectly marked. You should fill C=1024C = 1024, and the correct logarithmic expression is: log4(1024)=5\log_4(1024) = 5

Would you like to go over the other parts or have further clarifications?

Here are some related questions you might explore:

  1. What is the general relationship between exponents and logarithms?
  2. How can logarithms help solve exponential equations?
  3. What are the common logarithm bases used in practice?
  4. How can you calculate logarithms without a calculator?
  5. How does changing the base of a logarithm affect the value?

Tip: Remember that logarithms are the inverse operations of exponentiation.

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Math Problem Analysis

Mathematical Concepts

Exponents
Logarithms
Base of a Logarithm

Formulas

a^b = c is equivalent to log_a(c) = b

Theorems

Inverse relationship between exponents and logarithms

Suitable Grade Level

Grades 9-11