Solve the logarithmic equation log 9x 4 log 9x4 1 Select t

Solve the logarithmic equation. log 9(x + 4)+ log 9)(x-4) = 1 Select the correct choice below and. if necessary. fill in the answer box to complete your choice. x = (Simplify your answer. Use a comma to separate answers as needed.) There is no solution. Solve the following logarithmic equation. In x- In (x + 2) = 6 Select the correct choice below and. if necessary, fill in the answer box to complete your choice. (Round to four decimal places as needed. Use a comma to separate answers as needed.) There is no solution. A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 10 days. estimate the percentage of the original amount of the isotope released by the explosion that remains 2 days after the explosion. After 2 days, about j% of the isotope remains. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Solution

1) log9(x +4) +log9(x -4) = 1

use the property : loga +logb = log(a*b)

log9(x+4)(x-4) =1

x^2 - 16 =9

x^2 = 25

x = +/- 5

Only +5 is the solution as in logx , x>0

So, x = 5

2) lnx - ln(x +2) = 6

use the property : loga - logb = log(a/b)

ln(x/x+2) =6

x/(x+2) =e^6

x = xe^6 + 2e^6

x = 2e^6/( 1 - e^6)

= 2*403.4287/-402.428793

x = -2.0050