Question

What is the solution of in(x+6)-in9? Round your answer to the nearest hundredth.

x=53.50
x=60.50
x=66.50
x=72.50

Answer 1

ln (x+6) - ln 9 = 2

ln (x + 6)/9 = 2

(x + 6)/9 = e^2

x + 6 = 9e^2

x = 9e^2 - 6

x = 60.5

Answer: (B) x = 60.50

Answer 2

x =60.50 ( nearest hundredth).

Explanation:

Given : ln(x+6) - ln9 =2

To find : what is the solution up to nearest hundredth.

Solution : We have given that ln(x+6) - ln9=2

By the logarithm quotient rule ln (a+b) -lnc =
`ln(a+b)/(c)`.

`ln(x+6) -ln9` =
`ln(x+6)/(9)`.

`ln(x+6)/(9)` = 2

Taking exponent both side :

`e(ln(x+6)/(9))` =
`e^(2)`.

`(x+6)/(9)` = 7.38

On multiplying both side by 9

(x+6) = 9 * 7.38

x + 6 = 66.42

On subtracting by 6

x = 66.42 - 6

x = 60.42

x =60.50 ( nearest hundredth.)

Therefore, x =60.50 ( nearest hundredth).