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48∗4^𝑥+27=𝑎+𝑎∗4^𝑥+2

 Apr 8, 2020
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\(48∗4^𝑥+27=𝑎+𝑎∗4^𝑥+2\\ 48∗4^𝑥-𝑎∗4^𝑥=𝑎+2-27\\ 4^x(48-a)=𝑎-25\\ 2^{2x}(48-a)=𝑎-25\\ 2^{2x}=\frac{𝑎-25}{48-a}\\ log_2{2^{2x}}=log_2\frac{𝑎-25}{48-a}\\ 2x=log_2\left(\frac{𝑎-25}{48-a}\right)\\ x=\frac{1}{2}log_2\left(\frac{𝑎-25}{48-a}\right)\\\)

 

 

BUT you cannot find the log of a negative number so 

\(\frac{𝑎-25}{48-a}>0 \qquad and \quad 48-a\ne0\\ \frac{𝑎-25}{48-a}>0 \qquad and \quad a\ne48\\ 25

 

 

\(x=\frac{1}{2}log_2\left(\frac{𝑎-25}{48-a}\right)\qquad where\;\;25

 

Here is the graph

 

вот график

 

 

Coding:

48∗4^𝑥+27=𝑎+𝑎∗4^𝑥+2\\
48∗4^𝑥-𝑎∗4^𝑥=𝑎+2-27\\
4^x(48-a)=𝑎-25\\
2^{2x}(48-a)=𝑎-25\\
2^{2x}=\frac{𝑎-25}{48-a}\\
log_2{2^{2x}}=log_2\frac{𝑎-25}{48-a}\\
2x=log_2\left(\frac{𝑎-25}{48-a}\right)\\
x=\frac{1}{2}log_2\left(\frac{𝑎-25}{48-a}\right)\\

 

\frac{𝑎-25}{48-a}>0 \qquad and \quad 48-a\ne0\\
\frac{𝑎-25}{48-a}>0 \qquad and \quad a\ne48\\
 

 

x=\frac{1}{2}log_2\left(\frac{𝑎-25}{48-a}\right)\\\qquad where\;\;25

 Apr 8, 2020

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