Question

How do you solve `5^3 sqrt(4x - 2) = 17`?

Answer 1

`x = 0.504624`

Explanation:

Square both sides to get rid of the square root.

`(5^3sqrt(4x-2))^2 = 17^2`

`5^6 xx (4x-2) = 289`

`15625 (4x-2) = 289" "larr` isolate the bracket with `x`

`color(white)(xxxxxxxxxxxxxxxxxxxx)`Divide both sides by `15625`

`4x-2 = 289/15625" "larr` isolate the term in `x`

`4x = 289/15625 +2`

`4x = 2.018496" "larr div 4` to isolate `x`

`x = 2.018496/4`

`x = 0.504624`

Answer 2

If the intended equation was:

`5 root(3)(4x-2) = 17`

then `x = 5163/500 = 10.326`

Explanation:

Suppose the intended equation was:

`5 root(3)(4x-2) = 17`

We can cube both sides to get:

`125(4x-2) = 4913`

which multiplies out to get:

`500x-250 = 4913`

Add `250` to both sides to get:

`500x = 5163`

Divide both sides by `500` to get:

`x = 5163/500 = 10.326`

Answer 3

`color(magenta)(x=0.504624`

Explanation:

`5^3sqrt(4x-2)=17`

`:.sqrt(4x-2)=17/125`

Square both sides

`:.(sqrt(4x-2))^2=(17/125)^2`

`:.(sqrt(4x-2))^2=(0.136)^2`

`:.sqrtaxxsqrta=a`

`:.4x-2=0.018496`

`:.4x=2.018496`

`:.x=2.018496/4`

`:.color(magenta)(x=0.504624`

~~~~~~~~~~~~~~~~~

check:-

substitute `color(magenta)(x=0.504624`

`:.5^3sqrt(4(color(magenta)0.504624)-2)=17`

`:.125sqrt(0.018496)=17`

`:.125xx0.136=17`

`:.color(magenta)(17=17`