What is the answer to 8x-4=5x^{0.9} ?

The answer to 8x-4=5x^{0.9} is x=1.28109…

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8x-4=5x^{0.9}

8 x - 4 = 5 x^{0.9}

x = 1.28109 \dots

Solution steps

8 x - 4 = 5 x^{0.9}

Use the following exponent property

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

x^{0.9} = (x^{\frac{1}{10}})^{(0.9 \cdot 10)}

8 (x^{\frac{1}{10}})^{10} - 4 = 5 (x^{\frac{1}{10}})^{9}

Rewrite the equation with

x^{\frac{1}{10}} = u

8 u^{10} - 4 = 5 u^{9}

Solve

8 u^{10} - 4 = 5 u^{9} : u \approx 1.02508 \dots, u \approx - 0.88446 \dots

u \approx 1.02508 \dots, u \approx - 0.88446 \dots

Substitute back

u = x^{\frac{1}{10}},

solve for

x

Solve

x^{\frac{1}{10}} = 1.02508 \dots : x = 1.28109 \dots

Solve

x^{\frac{1}{10}} = - 0.88446 \dots :

No Solution for

x \in R

x = 1.28109 \dots

Verify Solutions:

x = 1.28109 \dots

True

The solution is

x = 1.28109 \dots

x = a x + b

13 = (6 - 1)^{2} + (y - 3)^{2}

(\frac{x}{1 - x})^{- 0.5} = 1.732

2 x - 1 = x + 1