What is the answer to 3^{2x}-10\times 3^x+21=0 ?

The answer to 3^{2x}-10\times 3^x+21=0 is x=(ln(7))/(ln(3)),x=1

Solve for x: 3^{2x}-10\times 3^x+21=0

The solution is x=(ln(7))/(ln(3)),x=1

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3^{2 x} - 10 \cdot 3^{x} + 21 = 0

x = \frac{ln ( 7 )}{ln ( 3 )}, x = 1

Decimal Notation

x = 1.77124 \dots, x = 1

Solution steps

3^{2 x} - 10 \cdot 3^{x} + 21 = 0

Apply exponent rules

(3^{x})^{2} - 10 \cdot 3^{x} + 21 = 0

Rewrite the equation with

3^{x} = u

(u)^{2} - 10 u + 21 = 0

Solve

u^{2} - 10 u + 21 = 0 : u = 7, u = 3

u = 7, u = 3

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 7 : x = \frac{ln ( 7 )}{ln ( 3 )}

Solve

3^{x} = 3 : x = 1

x = \frac{ln ( 7 )}{ln ( 3 )}, x = 1

3^{2 x - 4} = 3^{5 x + 8}

y, x = 1 2^{1 - 0.1 y}

9 9^{x + 9} = 999 9^{x + 9}

9 \cdot 2^{2 x} = 1

What is the answer to 3^{2x}-10\times 3^x+21=0 ?
The answer to 3^{2x}-10\times 3^x+21=0 is x=(ln(7))/(ln(3)),x=1
Solve for x: 3^{2x}-10\times 3^x+21=0
The solution is x=(ln(7))/(ln(3)),x=1