What is the answer to 2000(1.01)^x=1500(1.02)^x ?

The answer to 2000(1.01)^x=1500(1.02)^x is x=-(ln(3/4))/(ln(1.02)-ln(1.01))

Solve for x: 2000(1.01)^x=1500(1.02)^x

The solution is x=-(ln(3/4))/(ln(1.02)-ln(1.01))

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2000 (1.01)^{x} = 1500 (1.02)^{x}

x = - \frac{ln ( \frac{3}{4} )}{ln ( 1.02 ) - ln ( 1.01 )}

Decimal Notation

x = 29.19949 \dots

Solution steps

2000 (1.01)^{x} = 1500 (1.02)^{x}

Apply exponent rules

ln (2000) + x ln (1.01) = ln (1500) + x ln (1.02)

Solve

ln (2000) + x ln (1.01) = ln (1500) + x ln (1.02) : x = - \frac{ln ( \frac{3}{4} )}{ln ( 1.02 ) - ln ( 1.01 )}

x = - \frac{ln ( \frac{3}{4} )}{ln ( 1.02 ) - ln ( 1.01 )}

(1000) (1.05)^{3 x} = 3000

75 = 2 7^{x}

2^{3 x} = 4^{2 x - 1}

e^{7 x} = 17

lo g_{10} (x^{l o g_{10} (x)}) = 1

What is the answer to 2000(1.01)^x=1500(1.02)^x ?
The answer to 2000(1.01)^x=1500(1.02)^x is x=-(ln(3/4))/(ln(1.02)-ln(1.01))
Solve for x: 2000(1.01)^x=1500(1.02)^x
The solution is x=-(ln(3/4))/(ln(1.02)-ln(1.01))