# How to solve logarithm word problem given the exponential equation?

The question is

The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26%. The function that models this is $$y = 6.08(10)^{.0052t}$$ where y represents the population in billions and t is the time in years after 2000. Write and solve a logarithmic equation to determine what year the world population will exceed 7.5 billion.

So is the question asking me to convert the given equation into logarithmic equation than $$7.05 = 6.08(10)^{.0052t}$$ ( 7.5 billion is y right?) $$7.05/6.08 = 10^{.0052t}$$ $$1.15 = 10^{.0052t}$$ $$log(1.15) =.0052t$$ How would i even solve after that? is the way I've done so far good? how would i proceed after this than?

How do you solve the equation $$15 = 0.0052 t?$$
• @MATHASKER That's how logarithms work! $\log(10^x) = x$ – 5xum Nov 6 '15 at 1:04