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

2 Answers
Jim G.
May 3, 2017

#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"#

Jim H
May 3, 2017

#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) #

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