Answered

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Solve: [tex]4^{3x} = 4^2[/tex]

A. [tex]x = -\frac{3}{2}[/tex]
B. [tex]x = -\frac{2}{3}[/tex]
C. [tex]x = \frac{2}{3}[/tex]
D. [tex]x = \frac{3}{2}[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\( 4^{3x} = 4^2 \)[/tex], we can use the properties of exponents.

### Step-by-Step Solution:

1. Given equation:
[tex]\[ 4^{3x} = 4^2 \][/tex]

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

3. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{3} \][/tex]

### Conclusion:
The solution to the equation [tex]\( 4^{3x} = 4^2 \)[/tex] is [tex]\( x = \frac{2}{3} \)[/tex].

None of the other given options [tex]\(\left( x = -\frac{3}{2}, x = -\frac{2}{3}, x = \frac{3}{2} \right)\)[/tex] satisfy the equation.

Thus, the correct answer is:
[tex]\[ x = \frac{2}{3} \][/tex]
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