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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], we start by recognizing that 81 can be written as a power of 3. Specifically, [tex]\(81 = 3^4\)[/tex].

This transforms the given equation into:
[tex]\[3^{(3x-2)}=3^4\][/tex]

Since the bases are the same, we can set the exponents equal to each other:
[tex]\[3x - 2 = 4\][/tex]

To solve for [tex]\(x\)[/tex], we now solve the linear equation:
[tex]\[3x - 2 = 4\][/tex]

First, add 2 to both sides of the equation:
[tex]\[3x - 2 + 2 = 4 + 2\][/tex]
[tex]\[3x = 6\][/tex]

Next, divide both sides by 3:
[tex]\[x = \frac{6}{3}\][/tex]
[tex]\[x = 2\][/tex]

Therefore, the solution is:
[tex]\[3x - 2 = 4\][/tex]
and
[tex]\[x = 2\][/tex]
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