Question

what is 8^1/6 times 2^x = 32^1/2

what is the value of x

Answer 1

Hi there ! ♪┌|∵|┘♪

Answer: $\green{ \boxed{ \bf x = 2 + log_{2}(3) } }$

Step-by-step explanation:

$\bf \frac{ {8}^{1} }{6} \cdot {2}^{x} = \frac{ {32}^{1} }{2}$

$\bf \frac{8}{6} \times {2}^{x} = \frac{32}{2}$

$\bf \frac{4}{3} \times {2}^{x} = 16$

$\bf \frac{4 \times {2}^{x} }{3} = 16$

$\bf \frac{ {2}^{2} \times {2}^{x} }{3} = 16$

$\bf \frac{ {2}^{(x + 2)} }{3} = 16$

$\bf {2}^{(x + 2)} = 48$

$\bf x + 2 = log_{2}(48)$

$\bf x = log_{2}(48) - 2$

$\bf x = log_{2}(16 \times 3) - 2$

$\bf x = log_{2}(16) + log_{2}(3) - 2$

$\bf x = log_{2}({2}^{4} ) + log_{2}(3) - 2$

$\bf x = 4 + log_{2}(3) - 2 \Rightarrow \red{ \boxed{ \bf x = 2 + log_{2}(3) } }$