Question

question 18 (mandatory) (1 point) if 2^{3x}=64, then x is equal to a) 1 b) 3 c) 4 d) 2

Explanation:

Step1: Rewrite 64 as a power of 2

Since $64 = 2^6$, the equation $2^{3x}=64$ can be rewritten as $2^{3x}=2^6$.

Step2: Use exponent - equality rule

If $a^m=a^n$, then $m = n$. Here, $a = 2$, $m = 3x$ and $n = 6$. So, $3x=6$.

Step3: Solve for x

Divide both sides of the equation $3x = 6$ by 3. We get $x=\frac{6}{3}=2$.

Answer:

d) 2