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

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

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Answer 1 · 2017-05-03T14:51:40

$x \approx 37.12 to 2 decimal places$ $x~~37.12" to 2 decimal places"$

Explanation:

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

$∙ {log x}^{n} = n log x$ $• logx^n=nlogx$

$∙ {log}_{b} x = n \Leftrightarrow x = b^{n}$ $• log_b x=nhArrx=b^n$

$430 = x^{\frac{5}{3}} + 17$ $430=x^(5/3)+17$

$\Rightarrow x^{\frac{5}{3}} = 413$ $rArrx^(5/3)=413$

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

$\Rightarrow {ln x}^{\frac{5}{3}} = ln 413 \to using above law gives$ $rArrlnx^(5/3)=ln413rarr" using above law gives"$

$\frac{5}{3} ln x = ln 413$ $5/3lnx=ln413$

$\Rightarrow ln x = \frac{3}{5} ln 413 \to using above law$ $rArrlnx=3/5ln413rarr"using above law"$

$\Rightarrow x = e^{(\frac{3}{5} ln 413)} \approx 37.12 to 2 decimal places$ $rArrx=e^((3/5ln413))~~37.12" to 2 decimal places"$

Answer 2 · 2017-05-03T17:39:49

$x = 413^{\frac{3}{5}} = {\sqrt[5]{413}}^{3}$ $x=413^(3/5) = root(5)413^3$

Explanation:

$x^{\frac{5}{3}} + 17 = 430$ $x^(5/3)+17 = 430$

Subtract $17$ $17$ from both sides.

$x^{\frac{5}{3}} = 413$ $x^(5/3) = 413$

Raise both sides to the $\frac{3}{5}$ $3/5$ power

$x = 413^{\frac{3}{5}}$ $x=413^(3/5)$

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

2 Answers

Explanation:

Explanation:

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