Exponential and logarithmic growth: Logarithmic growth
Equations with logarithms
The logarithm allows us to write down solutions to equations like #4^x = 5# with unknown #x#; here: #x=\log_4(5)#.
Conversely, equations in which the unknown #x# only occurs through #\log_4(x)# can be solved by exponentiation of the answer. For example, the solution to the equation #\log_4(x) = \frac{5}{2}# is #x=32#.
Below we give some examples.
#x=32768#
Using the definition of the logarithm we can rewrite the equation as #x={8}^{5}=32768#.
Using the definition of the logarithm we can rewrite the equation as #x={8}^{5}=32768#.
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