What is the answer to 1.2x=8x^{0.12} ?

The answer to 1.2x=8x^{0.12} is x=0,x=-8.63495…,x=8.63495…

Solve for x: 1.2x=8x^{0.12}

The solution is x=0,x=-8.63495…,x=8.63495…

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1.2 x = 8 x^{0.12}

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

Solution steps

1.2 x = 8 x^{0.12}

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

x^{0.12} = (x^{\frac{1}{25}})^{(0.12 \cdot 25)}

1.2 (x^{\frac{1}{25}})^{25} = 8 (x^{\frac{1}{25}})^{3}

Rewrite the equation with

x^{\frac{1}{25}} = u

1.2 u^{25} = 8 u^{3}

Solve

1.2 u^{25} = 8 u^{3} : u = 0, u = - 1.09005 \dots, u = 1.09005 \dots

u = 0, u = - 1.09005 \dots, u = 1.09005 \dots

Substitute back

u = x^{\frac{1}{25}},

solve for

x

Solve

x^{\frac{1}{25}} = 0 : x = 0

Solve

x^{\frac{1}{25}} = - 1.09005 \dots : x = - 8.63495 \dots

Solve

x^{\frac{1}{25}} = 1.09005 \dots : x = 8.63495 \dots

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

Verify Solutions:

x = 0

True

, x = - 8.63495 \dots

True

, x = 8.63495 \dots

True

The solutions are

x = 0, x = - 8.63495 \dots, x = 8.63495 \dots

2 = 3 u - 12 - 1

x, y^{2} = x - 1

0.2 x^{\frac{1}{3}} = 0.062 x

x, f^{- 1} (x) = 2 x

x + x - 12 = 2

What is the answer to 1.2x=8x^{0.12} ?
The answer to 1.2x=8x^{0.12} is x=0,x=-8.63495…,x=8.63495…
Solve for x: 1.2x=8x^{0.12}
The solution is x=0,x=-8.63495…,x=8.63495…