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# Write the expoenential growth function with b=8. and find its inverse?

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Write the expoenential growth function with b=8. and find its inverse?

Guest Apr 22, 2017
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#1
+77147
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I assume that we have this ??

y  = a(b)^x

y = a(8)^x       divide both sides by a

(y / a)  =  (8)^x         take the log of both sides

log( y /a )  = log 8^x      and we can write

log ( y / a)   =  x * log 8     divide both sides by log 8

log ( y / a)  / log 8   = x       swap x and y

log ( x / a) / log 8  =  y        and for y,  write f-1 ( x)

f-1(x)  =   log ( x / a) / log 8

CPhill  Apr 22, 2017
#2
+1

$$y = a8^{x} \\ \frac{y}{a} = 8^{x} \\ (\frac{y}{a})^{\frac{1}{x}} = (8^{x})^{\frac{1}{x}} \\ (\frac{y}{a})^{\frac{1}{x}} = 8 \\ \frac{1}{x}ln(\frac{y}{a}) = ln(8) \\ \frac{1}{x}= \frac{ln(8)}{ln(\frac{y}{a})} \\ x = \frac{ln(\frac{y}{a})}{ln(8)}$$

Guest Apr 22, 2017

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