Exponential growth (easy(?) question):

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The discussion centers on calculating the number of years it will take for Morocco's GDP per capita, currently at $5,200, to equal France's GDP per capita of $35,500, given their respective growth rates of 3.5% and 1.1%. The equation to solve is 5200(1.035)^n = 35500(1.011)^n. By simplifying this to (1.035/1.011)^n = 35500/5200 and applying logarithms, one can determine the value of n, which represents the number of years required for the GDP per capita in Morocco to match that of France.

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Back to how income differences is explained in neoclassical theory, one can ask the question why GDP/capita is $5200 in Morocco and $35 500 in France. Real GDP per capita has grown at a rate of about 3.5% from 2008– 2012, GDP/capita in France grew in the same period at a rate of 1.1%. (http://data.worldbank.org/indicator/NY.GDP.PCAP.KD.ZG/countries/1W-XQ-EG-SY-IR-SA?display=default)
If this holds up GDP/ capita in Morocco will be the same as the one in France in X years.

So I can't find the X:

I have tried:

5200e^ln(1.035)t = 35 500e^ln(1.01)t

But I can't solve it..:-(

Hope someone can help me!:)
 
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The GDP per capita in Morocco after ##n## years will be ##5200(1.035)^n##, and in France it will be ##35500(1.011)^n##. Now set these equal to each other and solve for ##n##:
$$5200(1.035)^n = 35500(1.011)^n$$
or equivalently,
$$\left(\frac{1.035}{1.011}\right)^n = \frac{35500}{5200}$$
Taking logs of both sides should get you the answer quickly from here.