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Consider the equation below.

[tex]\( 3^{(3x-2)} = 81 \)[/tex]

To solve the given exponential equation, solve the linear equation [tex]\( 3x - 2 = \square \)[/tex].

The solution is [tex]\( x = \square \)[/tex].

Sagot :

GinnyAnswer
To solve the given exponential equation [tex]\( 3^{(3x - 2)} = 81 \)[/tex], follow these steps:

1. First, express 81 as a power of 3. We know that [tex]\( 81 = 3^4 \)[/tex].

Now the equation becomes:
[tex]\[ 3^{(3x - 2)} = 3^4 \][/tex]

2. Since the bases are the same, we can equate the exponents:
[tex]\[ 3x - 2 = 4 \][/tex]

3. Solve the linear equation [tex]\( 3x - 2 = 4 \)[/tex]:
- Add 2 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 3x = 4 + 2 \][/tex]
[tex]\[ 3x = 6 \][/tex]
- Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{6}{3} \][/tex]
[tex]\[ x = 2 \][/tex]

So, the solution to the given exponential equation is:
[tex]\[ 3x - 2 = 4 \][/tex]
[tex]\[ x = 2 \][/tex]
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