Question

What is the constant in

Answer 1

Answer:

Part a) $n=-8.017176$

Part b) $n=9.700465$

Step-by-step explanation:

Part a) we have

$9^{(n+10)}+3=81$

Solve for n

Subtract 3 both sides

$9^{(n+10)}+3-3=81-3$

$9^{(n+10)}=78$

take log both sides

$log[9^{(n+10)}]=log[78]$

$(n+10)log[9]=log[78]$

$(n+10)=log[78]/log[9]$

$n=\frac{log(78)}{log(9)}-10$ ----> using a calculator

$n=-8.017176$

Part b) we have

$11^{(n-8)}-5=54$

Solve for n

Adds 5 both sides

$11^{(n-8)}-5+5=54+5$

$11^{(n-8)}=59$

take log both sides

$log[11^{(n-8)}]=log[59]$

$(n-8)log[11]=log[59]$

$(n-8)=log[59]/log[11]$

$n=\frac{log(59)}{log(11)}+8$ ----> using a calculator

$n=9.700465$