4^3/4 x 2^x = 16^2/5 work out the exact value of x

Question

asked Dec 13, 2021 168k views

1 Answer

Wolendranh · Answer 1 · 2021-12-20T17:32:13+0000

Answer:

Explanation:

${4}^{ (3)/(4) } * {2}^(x) = {16}^{ (2)/(5) }$

In order to solve the equation express each of the terms in the same base .

in this case we express each of the terms in base 2

That's

${4}^{ (3)/(4) } = {2}^{2 * (3)/(4) } = {2}^{ (3)/(2) }$

And

${16}^{ (2)/(5) } = {2}^{4 * (2)/(5) } = {2}^{ (8)/(5) }$

So we have

${2}^{ (3)/(2) } * {2}^(x) = {2}^{ (8)/(5) }$

Since the left side are in the same base and are multiplying, we add the exponents

${2}^{ (3)/(2) + x } = {2}^{ (8)/(5) }$

Since they have the same base we can equate them

That's

(3)/(2) + x = (8)/(5)

x = (8)/(5) - (3)/(2)

x = (1)/(10)

Hope this helps you