https://file.aiquickdraw.com/mathbot/file/1726706616721h3jdx28d.jpg

The given expression is:

\[
\frac{2^{5\log \frac{1}{5}} + 9^{\log 3}}{9^{\log 3} \times 3^{\log 3}}
\]

Let's break this down step-by-step:

### Step 1: Simplify \( 2^{5 \log \frac{1}{5}} \)
We can use the property of logarithms \( a^{\log_b c} = c^{\log_b a} \).

Here, \( 2^{5 \log \frac{1}{5}} = \left( \frac{1}{5} \right)^{\log 2^5} = \left( \frac{1}{5} \right)^{\log 32} = \left( \frac{1}{5} \right)^{5 \log 2} \).

So, it becomes \( 32^{\log 5} = 5^{-5 \log 2} \).

### Step 2: Simplify \( 9^{\log 3} \)
Using the property \( a^{\log_b c} = c^{\log_b a} \), we get:
\[
9^{\log 3} = (3^2)^{\log 3} = 3^{2 \log 3} = 3^{2}
\]

### Step 3: Simplify \( 3^{\log 3} \)

\[
3^{\log 3} = 3^1 =1 
The full solution is:

`log`log 



Nilai dari \(\frac{2^{5\log\frac{1}{5}} + 9^{\log3}}{9^{\log3} \times 3^{\log3}}\) adalah ....

This problem involves simplifying logarithmic expressions using exponentiation rules and logarithmic identities. It tests concepts of exponent laws and logarithmic properties. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation