What is the answer to 3^x-6(sqrt(3))^x-27=0 ?

The answer to 3^x-6(sqrt(3))^x-27=0 is x=4

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3^x-6(sqrt(3))^x-27=0

3^{x} - 6 (3)^{x} - 27 = 0

x = 4

Solution steps

3^{x} - 6 (3)^{x} - 27 = 0

Apply exponent rules

3^{x} - 6 3^{x} - 27 = 0

Rewrite the equation with

3^{x} = u

u - 6 u - 27 = 0

Solve

u - 6 u - 27 = 0 : u = 81

u = 81

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 81 : x = 4

x = 4

2 5^{n + 1} = 5 \cdot 390625

2000 = 1000 (1 + 0.16)^{x}

7^{5 x + 10} = 7^{3 x - 4}

60 = 5 e^{2 x}

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

What is the answer to 3^x-6(sqrt(3))^x-27=0 ?
The answer to 3^x-6(sqrt(3))^x-27=0 is x=4
Solve for x: 3^x-6(sqrt(3))^x-27=0
The solution is x=4