SOLUTION: ln x+ln9x-20=1

Question 76241This question is from textbook algebra 2
: ln x+ln9x-20=1 This question is from textbook algebra 2

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
ln(x) + ln(9x) - 20 = 1
.
Adding logarithms is the same as multiplying. So ln(x) + ln(9x) is the same as ln(x*9x)
and multiplying x*9x results in 9x^2. So now the equation is:
.
ln(9x^2) - 20 = 1
.
Now add 20 to both sides and you get:
.
ln(9x^2) = 21
.
by switching to the exponential form this can be transformed to:
.
e^21 = 9x^2
.
Divide both sides by 9 and transpose to get:
.
x^2 = (e^21)/9
.
Now use a calculator to find that e^21 = 1318815734 and then dividing that by 9 you get
146535081.6
.
Substituting this for the right side of the equation results in:
.
x^2 = 146535081.6
.
Taking the square root of both sides results in x = 12105.16756
.
Check this out by substituting this value for x into the original problem. You get:
.
ln(12105.16756) + ln(9*12105.16756) - 20 = 1
.
Using a calculator you will find that ln(12105.16756) = 9.401387711 and ln(9*12105.16756)
is ln(108946.508) and your calculator will convert this to 11.59861229. Substituting
this into the equation results in:
.
9.401387711 + 11.59861229 - 20 = 1
.
The sum of the first two terms is 21. Substituting 21 in place of the two terms gives:
.
21 - 20 = 1
.
This equation balances which tells us that x does equal 12105.16756
.
Hope this helps you by providing one way to get a solution to this problem.
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