Answer:
Part a) [tex]n=-8.017176[/tex]
Part b) [tex]n=9.700465[/tex]
Step-by-step explanation:
Part a) we have
[tex]9^{(n+10)}+3=81[/tex]
Solve for n
Subtract 3 both sides
[tex]9^{(n+10)}+3-3=81-3[/tex]
[tex]9^{(n+10)}=78[/tex]
take log both sides
[tex]log[9^{(n+10)}]=log[78][/tex]
[tex](n+10)log[9]=log[78][/tex]
[tex](n+10)=log[78]/log[9][/tex]
[tex]n=\frac{log(78)}{log(9)}-10[/tex] ----> using a calculator
[tex]n=-8.017176[/tex]
Part b) we have
[tex]11^{(n-8)}-5=54[/tex]
Solve for n
Adds 5 both sides
[tex]11^{(n-8)}-5+5=54+5[/tex]
[tex]11^{(n-8)}=59[/tex]
take log both sides
[tex]log[11^{(n-8)}]=log[59][/tex]
[tex](n-8)log[11]=log[59][/tex]
[tex](n-8)=log[59]/log[11][/tex]
[tex]n=\frac{log(59)}{log(11)}+8[/tex] ----> using a calculator
[tex]n=9.700465[/tex]
