Answer:
[tex]a=4[/tex]
[tex]b=e^2[/tex]
Step-by-step explanation:
We are given that
[tex]f(x)=aln(bx)[/tex]
f(e)=12
f'(2)=2
We have to find the constants a and b
Substitute x=e
[tex]f(e)=aln(be)[/tex]
[tex]12=aln(be)[/tex]
[tex]ln(be)=\frac{12}{a}[/tex]
[tex]f'(x)=\frac{a}{x}[/tex]
Using the formula
d(lnx)/dx=1/x
[tex]f'(2)=\frac{a}{2}[/tex]
[tex]2=\frac{a}{2}[/tex]
[tex]a=4[/tex]
Substitute a=4
[tex]ln(be)=12/4=3[/tex]
[tex]be=e^{3}[/tex]
[tex]b=e^{3}/e[/tex]
[tex]b=e^2[/tex]
