What is the answer to 5^{2x}(3)-14(5^x)+8=0 ?

The answer to 5^{2x}(3)-14(5^x)+8=0 is x=(2ln(2))/(ln(5)),x=(ln(2/3))/(ln(5))

Solve for x: 5^{2x}(3)-14(5^x)+8=0

The solution is x=(2ln(2))/(ln(5)),x=(ln(2/3))/(ln(5))

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5^{2 x} (3) - 14 (5^{x}) + 8 = 0

x = \frac{2 ln ( 2 )}{ln ( 5 )}, x = \frac{ln ( \frac{2}{3} )}{ln ( 5 )}

Decimal Notation

x = 0.86135 \dots, x = - 0.25192 \dots

Solution steps

5^{2 x} (3) - 14 (5^{x}) + 8 = 0

Apply exponent rules

(5^{x})^{2} \cdot 3 - 14 \cdot 5^{x} + 8 = 0

Rewrite the equation with

5^{x} = u

(u)^{2} \cdot 3 - 14 u + 8 = 0

Solve

u^{2} \cdot 3 - 14 u + 8 = 0 : u = 4, u = \frac{2}{3}

u = 4, u = \frac{2}{3}

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 4 : x = \frac{2 ln ( 2 )}{ln ( 5 )}

Solve

5^{x} = \frac{2}{3} : x = \frac{ln ( \frac{2}{3} )}{ln ( 5 )}

x = \frac{2 ln ( 2 )}{ln ( 5 )}, x = \frac{ln ( \frac{2}{3} )}{ln ( 5 )}

2 0^{x} = 3

4^{x^{2}} \cdot 2^{7 x} = 16

4^{x + 1} + 2^{x - 2} = 68

- e^{x + 1} = 2 x + 1

5^{x} = 5^{2 x + 1}

What is the answer to 5^{2x}(3)-14(5^x)+8=0 ?
The answer to 5^{2x}(3)-14(5^x)+8=0 is x=(2ln(2))/(ln(5)),x=(ln(2/3))/(ln(5))
Solve for x: 5^{2x}(3)-14(5^x)+8=0
The solution is x=(2ln(2))/(ln(5)),x=(ln(2/3))/(ln(5))