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Logarithms 

hey can you do me a favour and check this for me 

the  number of gadgets sold in 2000 were 10 000 and in 2002, 82700 gadgets were sold growing exponentially. What year would the sales reach 500 000?

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Number of gadgets sold with exponential growth =

10 000 in 2000

82700 in 2002

500 000 in what year

Form: y = ab^x

Solve for a and b.

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82700 = ab^2

10000 = ab^0

a = 10000

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b^2 = 82700/10000

b^2 = 8.27

b = 2.8757

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Equation:

y = 10,000*2.8757^x

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Solve 10,000*2.8757^x > 500,000

2.8757^x > 50

x*log(2.8757) > log50

x > 3.7035 years

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Year 2000 + 3.7 = year 2004