Question

3\cdot 2^{\frac{x}{5}} = 150\
which of the following is the solution of the equation?\
choose 1 answer:\
a $x = 5\log_2(50)$\
b $x = 5\log_{50}(2)$\
c $x = \log_2(50)$\
d $x = \log_{50}(2)$

Explanation:

Step1: Isolate the exponential term

Divide both sides by 3:
$$2^{\frac{x}{5}} = \frac{150}{3} = 50$$

Step2: Convert to logarithmic form

Use $\log_b(a)=c \iff b^c=a$:
$$\frac{x}{5} = \log_2(50)$$

Step3: Solve for x

Multiply both sides by 5:
$$x = 5\log_2(50)$$

Answer:

A. $x = 5 \log_{2}(50)$