Math Problem Statement

1

2 log4 25 2 log4

ffiffiffiffiffi

20

Solution

It seems like there might be some formatting issues in the equation you've shared. I'll do my best to interpret it accurately, but if my interpretation is incorrect, please feel free to clarify.

Here's my interpretation based on the symbols provided:

  1. The expression starts with 11.
  2. Then, 2log4252 \log_4 25, which could be interpreted as "two times the logarithm of 25 with base 4."
  3. After that, there seems to be another term 2log42 \log_4.
  4. Finally, "ffiffiffiffiffi 20," which I interpret as a square root term, likely 20\sqrt{20}.

So, the expression might be:

1+2log425+2log4201 + 2 \log_4 25 + 2 \log_4 \sqrt{20}

Now, let's proceed to simplify this step-by-step.

Step-by-Step Solution

  1. Simplify each logarithmic term:

    • For 2log4252 \log_4 25: 2log425=log4252=log46252 \log_4 25 = \log_4 25^2 = \log_4 625

    • For 2log4202 \log_4 \sqrt{20}: 2log420=log4(20)2 \log_4 \sqrt{20} = \log_4 (20)

  2. Combine Terms: Now, combining the expression:

    1+log4625+log4201 + \log_4 625 + \log_4 20

  3. Use Logarithmic Properties to Simplify:

    1+log4(625×20)1 + \log_4 (625 \times 20)

If you could clarify or confirm this interpretation, I can continue with more detailed calculations and explanations based on that!

Would you like me to expand on these steps or provide additional details?


Here are five questions to further explore logarithmic expressions:

  1. How do we change the base of a logarithmic function?
  2. What are the properties of logarithmic functions when combining terms?
  3. How can logarithmic equations help in solving exponential equations?
  4. What are real-world applications of logarithms?
  5. How do we graph logarithmic functions?

Tip: Always remember that loga(xy)=logax+logay\log_a (x \cdot y) = \log_a x + \log_a y can simplify complex logarithmic expressions.

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Math Problem Analysis

Mathematical Concepts

Logarithms
Logarithmic Properties
Square Roots

Formulas

log_b (x * y) = log_b x + log_b y
log_b (x^n) = n * log_b x

Theorems

Properties of Logarithms
Product Rule for Logarithms
Power Rule for Logarithms

Suitable Grade Level

Grades 10-12