What is the answer to 7^{x+2}=410 ?

The answer to 7^{x+2}=410 is x=(ln(410))/(ln(7))-2

Solve for x: 7^{x+2}=410

The solution is x=(ln(410))/(ln(7))-2

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7^{x + 2} = 410

x = \frac{ln ( 410 )}{ln ( 7 )} - 2

Decimal Notation

x = 1.09169 \dots

Solution steps

7^{x + 2} = 410

Apply exponent rules

(x + 2) ln (7) = ln (410)

Solve

(x + 2) ln (7) = ln (410) : x = \frac{ln ( 410 )}{ln ( 7 )} - 2

x = \frac{ln ( 410 )}{ln ( 7 )} - 2

2^{3 x - 6} = 2^{x - 3}

1536 = 3 (2)^{n - 1}

3^{- 5 x} = 81

x, 2 7^{x} = 243

7^{x + 1} = 0

What is the answer to 7^{x+2}=410 ?
The answer to 7^{x+2}=410 is x=(ln(410))/(ln(7))-2
Solve for x: 7^{x+2}=410
The solution is x=(ln(410))/(ln(7))-2