What is the answer to 10^{2x}-5(10^x)+6=0 ?

The answer to 10^{2x}-5(10^x)+6=0 is x=(ln(3))/(ln(10)),x=(ln(2))/(ln(10))

Solve for x: 10^{2x}-5(10^x)+6=0

The solution is x=(ln(3))/(ln(10)),x=(ln(2))/(ln(10))

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1 0^{2 x} - 5 (1 0^{x}) + 6 = 0

x = \frac{ln ( 3 )}{ln ( 10 )}, x = \frac{ln ( 2 )}{ln ( 10 )}

Decimal Notation

x = 0.47712 \dots, x = 0.30102 \dots

Solution steps

1 0^{2 x} - 5 (1 0^{x}) + 6 = 0

Apply exponent rules

(1 0^{x})^{2} - 5 \cdot 1 0^{x} + 6 = 0

Rewrite the equation with

1 0^{x} = u

(u)^{2} - 5 u + 6 = 0

Solve

u^{2} - 5 u + 6 = 0 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = 1 0^{x},

solve for

x

Solve

1 0^{x} = 3 : x = \frac{ln ( 3 )}{ln ( 10 )}

Solve

1 0^{x} = 2 : x = \frac{ln ( 2 )}{ln ( 10 )}

x = \frac{ln ( 3 )}{ln ( 10 )}, x = \frac{ln ( 2 )}{ln ( 10 )}

200 = 2^{x}

1 6^{x + 2} = 8^{x - 1}

4^{- x + 2} = 3^{2 x - 1}

3^{n + 3} = 9^{n}

7^{n + 2} + 4 9^{n + 1} = 120050

What is the answer to 10^{2x}-5(10^x)+6=0 ?
The answer to 10^{2x}-5(10^x)+6=0 is x=(ln(3))/(ln(10)),x=(ln(2))/(ln(10))
Solve for x: 10^{2x}-5(10^x)+6=0
The solution is x=(ln(3))/(ln(10)),x=(ln(2))/(ln(10))