Write the exponential equation in logarithmic form. For example, the logarithmic form of $$ 2^{3}=8 $$ is $$ \log _{2}(8)=3 $$. $$ 32^{2 / 5}=4 $$ Need Help? Read It Watch It

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To convert the exponential equation $$ 32^{\frac{2}{5}} = 4 $$ into its logarithmic form, you can follow the structure of the example you provided.

**General Form:**
$$ a^b = c \quad \text{is equivalent to} \quad \log_a(c) = b $$

**Applying to Your Equation:**
$$ 32^{\frac{2}{5}} = 4 $$

**Logarithmic Form:**
$$ \log_{32}(4) = \frac{2}{5} $$

**Explanation:**
- **Base $$ a $$:** In the exponential form, the base is 32.
- **Exponent $$ b $$:** The exponent is $$ \frac{2}{5} $$.
- **Result $$ c $$:** The result of the exponential equation is 4.

So, the logarithmic form reads as "the logarithm base 32 of 4 is equal to $$ \frac{2}{5} $$", which is written mathematically as:
$$ \log_{32}(4) = \frac{2}{5} $$

This means that you need to raise 32 to the power of $$ \frac{2}{5} $$ to get 4.
The logarithmic form of $$ 32^{\frac{2}{5}} = 4 $$ is $$ \log_{32}(4) = \frac{2}{5} $$.

Write the exponential equation in logarithmic form. For example, the logarithmic form of \( 2^{3}=8 \) is \( \log _{2}(8)=3 \). \( 32^{2 / 5}=4 \) Need Help? Read It Watch It

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