logs...can someone please help?!?!?!?!?

Question

ok here are some problems that I'm completely stuck on..can someone help if you know atleast one that would be great I just need help on these six..Thanks

Here I need to condense each expression to a single term.

2 ln (x+2)- ln x

1/2 x log x + log 3 (x+1)

Here I need a single log expression:

Square root sign and under neath it is 3x -5 / 7

4x square root sign and underneath is 10x - 3x

Here I need to solve the exponential equation :

2 log base 5 3x = 4

log base 3 + log base 3 (x squared -8) = log base 3 8 x

Answer 1

2 ln(x+2) - ln x
= ln(x+2)^2 - ln x
= ln ((x+2)^2)/x

1/2 log x + log 3(x+1)
= log x^(1/2) + log 3(x+1)
= log 3(x+1)(x^(1/2))

sqrt(y) = 3x-5/7
y = (3x-5)^2/49

4 x sqrt(y) = 10x-3x
4 x sqrt(y) = 7x
sqrt(y) = 7x/4
y = 49x^2/16

2 log base 5 3x = 4
log base 5 3x = 2
3x = 5^2
3x = 25
x = 25/3

log base 3 + log base 3 (x^2 - 8) = log base 3 8x
log base 3 (x^2 - 8) = log base 3 8x
x^2 - 8 = 8x
x^2 - 8x - 8 =0

x = (8+/-sqrt(8^2 - 4(1)(-8)))/2(1)
x = (8 +/- sqrt(96))/2
x = 4 +- 2(sqrt(6))

Answer 2

The way you've laid out the questions make it really difficult to tell when you're multiplying two logs together or when that "X" represents a variable instead of the multiplication sign.

Look at how others have written out logs on here and try to do the same ok?

And when you write something as squared you say x^2
" ^ " is above the 6 on your keyboard