Math Problem Statement

Nilai dari 2log20 + 2log45 - 2log180 - 2log40 adalah...

Solution

The image shows a mathematical expression involving logarithms. The expression is written as:

\text{Nilai dari } \, ^2\log 20 + ^2\log 45 - ^2\log 180 - ^2\log 40 \, \text{adalah} \ldots

This seems to be using base-2 logarithms (denoted as 2log^2\log).

We can solve this expression using logarithmic properties:

2log20+2log452log1802log40^2\log 20 + ^2\log 45 - ^2\log 180 - ^2\log 40

Step-by-step simplification:

  1. Use the logarithmic sum property: 2loga+2logb=2log(a×b)^2\log a + ^2\log b = ^2\log (a \times b) So: 2log20+2log45=2log(20×45)=2log900^2\log 20 + ^2\log 45 = ^2\log (20 \times 45) = ^2\log 900

  2. **Use

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Math Problem Analysis

Mathematical Concepts

Logarithms
Logarithmic Properties
Algebra

Formulas

log(a) + log(b) = log(a * b)
log(a) - log(b) = log(a / b)

Theorems

Logarithmic Addition and Subtraction

Suitable Grade Level

Grades 9-12