Question

Math

Posted 3 months ago

```
Solve the logarithmic equation $\log _{3}(81)=x$
$x=7$
$x=4$
$x=27$
$x=3$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To solve the logarithmic equation $\log_{3}(81) = x$, we need to express 81 as a power of 3

step 2

We know that $81 = 3^4$

step 3

Therefore, $\log_{3}(81) = \log_{3}(3^4)$

step 4

Using the property of logarithms, $\log_{b}(b^k) = k$, we get $\log_{3}(3^4) = 4$

step 5

Hence, $x = 4$

Answer

$x = 4$

Key Concept

Logarithmic properties

Explanation

The logarithmic property $\log_{b}(b^k) = k$ allows us to simplify the expression $\log_{3}(81)$ by expressing 81 as $3^4$, leading to the solution $x = 4$.

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