solve the equation ln(x)- ln (x-3) = ln(5)

combining logs...



raising e to both sides of the equation...

which leads to...




and so...

Solve: log(x+4) + log(x)=9

Combining into one log...




raise 10 to both sides of the equation...



After solving we note that only positive numbers are solutions (Why?)

Solve: log3(x+3)+log3(x-3)=3

 <--other solution is extraneous

Find the value of x: log6 (5x + 9)= 4

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log7 ( ¼w + 40) = 2; w = _______________

raise 7 to both sides to get:

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Solve: Log(5+x)-log(x-2)=log2

 

If y=-7log5(2x), find inverse function.

so the inverse is

Solve: log3 (x+10) + log3 (x+25)=1

log3 (x+10) + log3 (x+25)=1
log3 (x+10)(x+25)=1
3^log3 (x+10)(x+25)=3^1
x^2+35x+250=3
x^2+35x+247=0

Solve: ln(x+1)-ln(x-2)=ln(2)

Solve for x

2ln 2 +ln(x-5)=ln40

2ln 2 +ln(x-5)=ln40
ln(x-5)=ln40-2ln 2
ln(x-5)=ln10
x-5=10
x=15

Solve for x: log2(x-2)=log4(x)

 


 

 


which has solutions x=1 and x=4. But x=1 is extraneous 
...so x=4

Solve: 2ln3x+ln2=lnx

ln2=lnx-2ln3x
lnx-2ln3x=ln2
ln(x/(3x)^2)=ln2
e^ln(x/(3x)^2)=e^ln2
x/(9x^2)=2
1/(9x)=2
x=1/18

Solve for x y=3ln(3x)

 

 
 

How do I solve 5+2ln(x)=8