What is the answer to (27)^x=3^x+6 ?

The answer to (27)^x=3^x+6 is x=(ln(2))/(ln(3))

Solve for x: (27)^x=3^x+6

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

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(27)^{x} = 3^{x} + 6

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

Decimal Notation

x = 0.63092 \dots

Solution steps

(27)^{x} = 3^{x} + 6

Apply exponent rules

(3^{x})^{3} = 3^{x} + 6

Rewrite the equation with

3^{x} = u

(u)^{3} = u + 6

Solve

u^{3} = u + 6 : u = 2

u = 2

Substitute back

u = 3^{x},

solve for

x

Solve

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

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

1 0^{x} = 5

3^{x} + 3 + 3^{x} - 27 = 2241

1 0^{x} = 2

7^{2 x} - 7^{x + 1} - 8 = 0

3 \cdot 8 1^{x} = 9^{x + 4}

What is the answer to (27)^x=3^x+6 ?
The answer to (27)^x=3^x+6 is x=(ln(2))/(ln(3))
Solve for x: (27)^x=3^x+6
The solution is x=(ln(2))/(ln(3))