Solve for x 2(x-1)^(1/5)=(2x-17)^(1/5)

$2 {(x - 1)}^{\frac{1}{5}} = {(2 x - 17)}^{\frac{1}{5}}$

Divide each term in $2 {(x - 1)}^{\frac{1}{5}} = {(2 x - 17)}^{\frac{1}{5}}$ by $2$ and simplify.

Divide each term in $2 {(x - 1)}^{\frac{1}{5}} = {(2 x - 17)}^{\frac{1}{5}}$ by $2$ .

$\frac{2 {(x - 1)}^{\frac{1}{5}}}{2} = \frac{{(2 x - 17)}^{\frac{1}{5}}}{2}$

Simplify the left side.

Cancel the common factor.

$\frac{2 {(x - 1)}^{\frac{1}{5}}}{2} = \frac{{(2 x - 17)}^{\frac{1}{5}}}{2}$

Divide ${(x - 1)}^{\frac{1}{5}}$ by $1$ .

${(x - 1)}^{\frac{1}{5}} = \frac{{(2 x - 17)}^{\frac{1}{5}}}{2}$

Eliminate the fractional exponents by multiplying both exponents by the LCD.

${({(x - 1)}^{\frac{1}{5}})}^{5} = {(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$

Simplify ${({(x - 1)}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(x - 1)}^{\frac{1}{5}})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x - 1)}^{\frac{1}{5} \cdot 5} = {(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(x - 1)}^{\frac{1}{5} \cdot 5} = {(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$

Rewrite the expression.

${(x - 1)}^{1} = {(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$

Simplify.

$x - 1 = {(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$

Simplify ${(\frac{{(2 x - 17)}^{\frac{1}{5}}}{2})}^{5}$ .

Apply the product rule to $\frac{{(2 x - 17)}^{\frac{1}{5}}}{2}$ .

$x - 1 = \frac{{({(2 x - 17)}^{\frac{1}{5}})}^{5}}{2^{5}}$

Simplify the numerator.

Multiply the exponents in ${({(2 x - 17)}^{\frac{1}{5}})}^{5}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x - 1 = \frac{{(2 x - 17)}^{\frac{1}{5} \cdot 5}}{2^{5}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x - 1 = \frac{{(2 x - 17)}^{\frac{1}{5} \cdot 5}}{2^{5}}$

Rewrite the expression.

$x - 1 = \frac{{(2 x - 17)}^{1}}{2^{5}}$

Simplify.

$x - 1 = \frac{2 x - 17}{2^{5}}$

Raise $2$ to the power of $5$ .

$x - 1 = \frac{2 x - 17}{32}$

Multiply both sides by $32$ .

$(x - 1) \cdot 32 = \frac{2 x - 17}{32} \cdot 32$

Simplify.

Simplify the left side.

Simplify $(x - 1) \cdot 32$ .

Apply the distributive property.

$x \cdot 32 - 1 \cdot 32 = \frac{2 x - 17}{32} \cdot 32$

Simplify the expression.

Move $32$ to the left of $x$ .

$32 \cdot x - 1 \cdot 32 = \frac{2 x - 17}{32} \cdot 32$

Multiply $- 1$ by $32$ .

$32 x - 32 = \frac{2 x - 17}{32} \cdot 32$

Simplify the right side.

Cancel the common factor of $32$ .

Cancel the common factor.

$32 x - 32 = \frac{2 x - 17}{32} \cdot 32$

Rewrite the expression.

$32 x - 32 = 2 x - 17$

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$32 x - 32 - 2 x = - 17$

Subtract $2 x$ from $32 x$ .

$30 x - 32 = - 17$

Move all terms not containing $x$ to the right side of the equation.

Add $32$ to both sides of the equation.

$30 x = - 17 + 32$

Add $- 17$ and $32$ .

$30 x = 15$

Divide each term in $30 x = 15$ by $30$ and simplify.

Divide each term in $30 x = 15$ by $30$ .

$\frac{30 x}{30} = \frac{15}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 x}{30} = \frac{15}{30}$

Divide $x$ by $1$ .

$x = \frac{15}{30}$

Simplify the right side.

Cancel the common factor of $15$ and $30$ .

Factor $15$ out of $15$ .

$x = \frac{15 (1)}{30}$

Cancel the common factors.

Factor $15$ out of $30$ .

$x = \frac{15 \cdot 1}{15 \cdot 2}$

Cancel the common factor.

$x = \frac{15 \cdot 1}{15 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x 2(x-1)^(1/5)=(2x-17)^(1/5)

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