What is the answer to 25^x-8*5^x=-16 ?

The answer to 25^x-8*5^x=-16 is x=(2ln(2))/(ln(5))

Solve for x: 25^x-8*5^x=-16

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

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2 5^{x} - 8 \cdot 5^{x} = - 16

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

Decimal Notation

x = 0.86135 \dots

Solution steps

2 5^{x} - 8 \cdot 5^{x} = - 16

Apply exponent rules

(5^{x})^{2} - 8 \cdot 5^{x} = - 16

Rewrite the equation with

5^{x} = u

(u)^{2} - 8 u = - 16

Solve

u^{2} - 8 u = - 16 : u = 4

u = 4

Substitute back

u = 5^{x},

solve for

x

Solve

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

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

5^{x + 4} = 12 5^{x - 4}

6^{x} = 47

- 56 e^{- 8 x^{7}} x^{6} = 0

4^{x - 2} = 1 6^{x + 1}

5 \times 2^{x + 3} = \frac{5}{4}

What is the answer to 25^x-8*5^x=-16 ?
The answer to 25^x-8*5^x=-16 is x=(2ln(2))/(ln(5))
Solve for x: 25^x-8*5^x=-16
The solution is x=(2ln(2))/(ln(5))