What is the answer to 500*2^d=50*3^d ?

The answer to 500*2^d=50*3^d is d=(ln(10))/(ln(3)-ln(2))

Solve for d: 500*2^d=50*3^d

The solution is d=(ln(10))/(ln(3)-ln(2))

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500 \cdot 2^{d} = 50 \cdot 3^{d}

d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}

Decimal Notation

d = 5.67887 \dots

Solution steps

500 \cdot 2^{d} = 50 \cdot 3^{d}

Apply exponent rules

ln (500) + d ln (2) = ln (50) + d ln (3)

Solve

ln (500) + d ln (2) = ln (50) + d ln (3) : d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}

d = \frac{ln ( 10 )}{ln ( 3 ) - ln ( 2 )}

3 e^{- 2 x} = 75

8 1^{2^{x + 7}} = 2^{8^{x - 13}}

1 5^{x} = 20

x^{x} = x^{2 x - 1}

2200 (1.04)^{x} = 8000

What is the answer to 500*2^d=50*3^d ?
The answer to 500*2^d=50*3^d is d=(ln(10))/(ln(3)-ln(2))
Solve for d: 500*2^d=50*3^d
The solution is d=(ln(10))/(ln(3)-ln(2))