Question

How do you solve `430= x ^ { \frac { 5} { 3} } + 17`?

Answer 1

`x~~37.12" to 2 decimal places"`

Explanation:

`"using the "color(blue)"laws of logarithms"`

`• logx^n=nlogx`

`• log_b x=nhArrx=b^n`

`430=x^(5/3)+17`

`rArrx^(5/3)=413`

`"take the ln (natural log.) of both sided"`

`rArrlnx^(5/3)=ln413rarr" using above law gives"`

`5/3lnx=ln413`

`rArrlnx=3/5ln413rarr"using above law"`

`rArrx=e^((3/5ln413))~~37.12" to 2 decimal places"`

Answer 2

`x=413^(3/5) = root(5)413^3`

Explanation:

`x^(5/3)+17 = 430`

Subtract `17` from both sides.

`x^(5/3) = 413`

Raise both sides to the `3/5` power

`x=413^(3/5)`