Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.