What is the answer to 25^x-9*5^x+20=0 ?

The answer to 25^x-9*5^x+20=0 is x=1,x=(2ln(2))/(ln(5))

Solve for x: 25^x-9*5^x+20=0

The solution is x=1,x=(2ln(2))/(ln(5))

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2 5^{x} - 9 \cdot 5^{x} + 20 = 0

x = 1, x = \frac{2 ln ( 2 )}{ln ( 5 )}

Decimal Notation

x = 1, x = 0.86135 \dots

Solution steps

2 5^{x} - 9 \cdot 5^{x} + 20 = 0

Apply exponent rules

(5^{x})^{2} - 9 \cdot 5^{x} + 20 = 0

Rewrite the equation with

5^{x} = u

(u)^{2} - 9 u + 20 = 0

Solve

u^{2} - 9 u + 20 = 0 : u = 5, u = 4

u = 5, u = 4

Substitute back

u = 5^{x},

solve for

x

Solve

5^{x} = 5 : x = 1

Solve

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

x = 1, x = \frac{2 ln ( 2 )}{ln ( 5 )}

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

(\frac{1}{2})^{x} = \frac{1}{16}

78 \cdot 1.05 5^{t} = 110

g (p) = 4^{x}, x = \frac{3}{2}

3 (2^{x}) = 48

What is the answer to 25^x-9*5^x+20=0 ?
The answer to 25^x-9*5^x+20=0 is x=1,x=(2ln(2))/(ln(5))
Solve for x: 25^x-9*5^x+20=0
The solution is x=1,x=(2ln(2))/(ln(5))