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Ilia_Sergeevich [38]
3 years ago
8

Need help please find the inverse of this logarithm function please ❤️ ONLY IF UR GOOD AT MATH!!!!

Mathematics
2 answers:
SSSSS [86.1K]3 years ago
8 0

as you already know, we start by doing a quick switcheroo on the variables, to get the inverse expression of any expression, so


\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{f(x)}{y}=3\left( 2^{x+3} \right)-4\implies \stackrel{\textit{quick switcheroo}}{x=3\left( 2^{y+3} \right)-4}\implies x+4=3\left( 2^{y+3} \right)


\bf \cfrac{x+4}{3}=2^{y+3}\implies \log\left( \cfrac{x+4}{3} \right)=\log\left( 2^{y+3} \right) \\\\\\ \log\left( \cfrac{x+4}{3} \right)=(y+3)\log\left( 2 \right)\implies \cfrac{\log\left( \frac{x+4}{3} \right)}{\log(2)}=y+3 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{\log\left( \frac{x+4}{3} \right)}{\log(2)}-3=\stackrel{f^{-1}(x)}{y}~\hfill

kykrilka [37]3 years ago
3 0

Answer:

f-1(x) = log2 [ (x + 4)/3 ] - 3.

Step-by-step explanation:

Let y = 3(2^(x+3) - 4

3(2^(x + 3) = y + 4

2^(x + 3) = (y + 4)/3

x + 3 = log2 [(y + 4)/3]

x = log2 [ (y + 4)/3 ] - 3

Inverse f-1(x) = log2 [ (x + 4)/3 ] - 3




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a_n=1 + (-\frac{4}{9} )^n\\\\When\ n=1:a_1=1 + (-\frac{4}{9} )^1=0.5556\\\\When\ n=2:a_2=1 + (-\frac{4}{9} )^2=1.1975\\\\When\ n=3:a_3=1 + (-\frac{4}{9} )^3=0.9122\\\\When\ n=4:a_4=1 + (-\frac{4}{9} )^4=1.039\\\\When\ n=5:a_5=1 + (-\frac{4}{9} )^5=0.9827\\\\When\ n=6:a_6=1 + (-\frac{4}{9} )^6=1.0077\\\\When\ n=7:a_7=1 + (-\frac{4}{9} )^7=0.9966\\\\When\ n=8:a_8=1 + (-\frac{4}{9} )^8=1.0015\\\\When\ n=9:a_9=1 + (-\frac{4}{9} )^9=0.9993\\\\

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