SOLUTION: good morning
would you help me find the logarithmic equation
6+ln(8x)=24-2 ln(x)
Algebra.Com
Question 1059970: good morning
would you help me find the logarithmic equation
6+ln(8x)=24-2 ln(x)
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
6+ln(8x)=24-2 ln(x)
---------------------------
ln(8x)+ln(x^2) = 24-6
------------------------
ln[x^2*8x] = 18
----
8x^3 = e^18
-----
x^3 = e^18/8
------
x = (e^6)/2
------
x = 210.71
-------------
Cheers,
Stan H.
---------------
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Solve for x over the real numbers
:
6 + ln(8x) = 24 - 2ln(x)
:
Subtract 24 - 2 ln(x) from both sides
:
-18 + 2ln(x) + ln(8x) = 0
:
-18 + 2ln(x) + ln(8x) = -18 + ln(8x) + ln(x^2) = ln(8x^3) - 18
:
Note that c(ln(x)) = ln(x^c) where c is a constant, then we use the product rule of logarithms
:
ln(8x^3) - 18 = 0
:
Add 18 to both sides
:
ln(8x^3) = 18
:
Cancel logarithms by taking exp of both sides, note that ln is natural logarithm
:
8x^3 = e^18
:
Divide both sides by 8
:
x^3 = e^18/8
:
Take cube roots of both sides
:
**********************************************
x = e^6/2
:
Note that e is approximately 2.71828
:
x = (2.71828)^6 / 2 is approximately 201.7144
**********************************************
:
RELATED QUESTIONS
The problem says to solve the logarithmic equation:
5 + ln (8x) = 23 - 2 ln... (answered by solver91311)
Hello,
Could you help me solve this logarithmic equation using property of equality?... (answered by TimothyLamb)
how do you solve the logarithmic equation ln x - ln (x - 3)= ln... (answered by stanbon)
Can you please help me with this equation?
ln(x-5)-ln(x+4)=... (answered by scott8148)
Write as a single logarithm and check with a calculator
a) ln 5 + ln 3
b) ln 2+ ln 10... (answered by jim_thompson5910,stanbon)
Solve the logarithmic or exponential equation.
ln(x +1) − ln(x − 2) = ln... (answered by jim_thompson5910)
solve the following logarithmic equation
ln(x)=... (answered by solver91311)
simplify the expression.
ln(x^2+8x+15)-ln(x+3)
thank you for the... (answered by Fombitz)
Consider the following equation.
ln(x) + ln(x + 6) = 4
Solve the logarithmic equation (answered by stanbon)