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Popular >

2^k*7^d=392

Solution

2^{k} \cdot 7^{d} = 392

Solution

d = \frac{2 ln ( 7 ) + ln ( 2 ) ( - k + 3 )}{ln ( 7 )}

Solution steps

2^{k} \cdot 7^{d} = 392

Divide both sides by

2^{k}

7^{d} = \frac{392}{2 ^{k}}

Simplify

\frac{392}{2 ^{k}} : 49 \cdot 2^{3 - k}

7^{d} = 49 \cdot 2^{3 - k}

Apply exponent rules

d ln (7) = ln (49 \cdot 2^{3 - k})

Solve

d ln (7) = ln (49 \cdot 2^{3 - k}) : d = \frac{2 ln ( 7 ) + ln ( 2 ) ( - k + 3 )}{ln ( 7 )}

d = \frac{2 ln ( 7 ) + ln ( 2 ) ( - k + 3 )}{ln ( 7 )}

Popular Examples

9*3^x=(27)^{2x-5}

9 \cdot 3^{x} = (27)^{2 x - 5}

7^{4sqrt(x)}-8*7^{sqrt(4x)}+7=0

7^{4 x} - 8 \cdot 7^{4 x} + 7 = 0

solvefor a,(x^6)/(x^a)=x^8 solve for

a, \frac{x ^{6}}{x ^{a}} = x^{8}

1 5^{y + 6} = 2

5^{x} + 5^{x + 1} = 30

Frequently Asked Questions (FAQ)

What is the answer to 2^k*7^d=392 ?
The answer to 2^k*7^d=392 is d=(2ln(7)+ln(2)(-k+3))/(ln(7))