What is the answer to 2^{5k+3}=3^{550} ?

The answer to 2^{5k+3}=3^{550} is k=(550ln(3)-3ln(2))/(5ln(2))

Solve for k: 2^{5k+3}=3^{550}

The solution is k=(550ln(3)-3ln(2))/(5ln(2))

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2^{5 k + 3} = 3^{550}

k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

Decimal Notation

k = 173.74587 \dots

Solution steps

2^{5 k + 3} = 3^{550}

Apply exponent rules

(5 k + 3) ln (2) = 550 ln (3)

Solve

(5 k + 3) ln (2) = 550 ln (3) : k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

k = \frac{550 ln ( 3 ) - 3 ln ( 2 )}{5 ln ( 2 )}

b, a^{b} = 144 a - 1

8^{x} = 3 2^{2 x + 2}

\frac{3 ^{\frac{x}{2}} + 3}{3 ^{\frac{x}{2}}} = 4

2^{t} = 0

1 0^{c} = 10000

What is the answer to 2^{5k+3}=3^{550} ?
The answer to 2^{5k+3}=3^{550} is k=(550ln(3)-3ln(2))/(5ln(2))
Solve for k: 2^{5k+3}=3^{550}
The solution is k=(550ln(3)-3ln(2))/(5ln(2))