+118696 48∗4𝑥+27=𝑎+𝑎∗4𝑥+248∗4𝑥−𝑎∗4𝑥=𝑎+2−274x(48−a)=𝑎−2522x(48−a)=𝑎−2522x=𝑎−2548−alog222x=log2𝑎−2548−a2x=log2(𝑎−2548−a)x=12log2(𝑎−2548−a)
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
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
