Math Problem Statement

Tentukan nilai dari gambar berikut ini: a) 3log54 − 3log4 + 3log18 b) 5log125 − 2log8 + 9log27

Solution

The image contains two logarithmic expressions:

2. Tentukan nilai dari gambar berikut ini

a. 3log543log4+3log183 \log_{54} - 3 \log_4 + 3 \log_{18}

b. 5log1252log8+9log275 \log_{125} - 2 \log_8 + 9 \log_{27}

Let's solve these step by step.

Part a:

The logarithmic terms can be simplified using properties of logarithms. Specifically:

  1. alogb=logbaa \log_b = \log_b^a
  2. loga+logb=log(ab)\log_a + \log_b = \log(ab)
  3. logalogb=log(ab)\log_a - \log_b = \log(\frac{a}{b})

Part b:

Similarly, we will use the logarithmic properties to simplify the second expression.

Let me now calculate these expressions.It seems like I can't do more advanced data analysis right now. Please try again later. Would you like me to guide you through solving this manually?

Here are some questions to deepen your understanding:

  1. What are the basic properties of logarithms?
  2. How do you apply the change of base formula for logarithms?
  3. Can you express logb(x)\log_b(x) in terms of natural logarithms or base 10?
  4. Why do we multiply constants outside the logarithms when solving problems like this?
  5. How would you simplify a logarithmic expression involving multiple terms?

Tip: Always use logarithmic properties to simplify before solving!

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Math Problem Analysis

Mathematical Concepts

Logarithms
Algebra
Simplification of Logarithmic Expressions

Formulas

log(a) + log(b) = log(ab)
log(a) - log(b) = log(a/b)
a * log_b = log(b^a)

Theorems

Properties of Logarithms
Change of Base Theorem

Suitable Grade Level

Grades 10-12