Question

8^1/6 x2^x=32^1/2 work out the exact value of x

Answer 1

Answer:

i hope that helps......

Answer 2

For the given equation, the value of $x$ is $2$.

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

$(2^{3})^{\frac{1}{6}} \times 2^{x} = (2^{5})^{\frac{1}{2}}$

$2^{\frac{1}{2}} \times 2^{x} = 2^{\frac{5}{2}}$

$2^{\frac{1}{2}+x}=2^{\frac{5}{2}}$

Since, the bases are equal, we can compare the powers.

$\frac{1}{2}+x=\frac{5}{2}$

$x=\frac{5}{2}-\frac{1}{2}$

$x=\frac{5-1}{2}$

$x=\frac{4}{2}$

$x=2$

So, the value of $x$ is $2$.

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