Logrithm problem help?

Question

2Log (base 2) of X -- Log (base 2) of (X+3) = 2

please help, and show how its done. thank you so much.

Answer 1

Hi,

2Log (base 2) of X -- Log (base 2) of (X+3) = 2

Log (base 2) of X^2 -- Log (base 2) of (X+3) = 2

...............................X^2
Log (base 2) of -------- = 2
............................(X+3)

Putting this into exponential form makes it:

..x^2
-------- = 2^2
x + 3

..x^2
-------- = 4
x + 3

x^2 = 4(x + 3)

x^2 = 4x + 12

x^2 - 4x - 12 = 0

(x - 6)(x + 2) = 0

x = 6 or x = -2 but you can't take the log of a negative number so eliminate x = -2. Therefore, the only answer is x = 6.

I hope that helps!! :-)

Answer 2

In following solution assume log x means log base two x:-
2.log x - log (x + 3) = 2
log x² - log (x + 3) = 2
x² / (x + 3) = 4
x² = 4x + 12
x² - 4x - 12 = 0
(x - 6).(x + 2) = 0
x = 6 (accepting + ve value for x)

Answer 3

2Log (base 2) of X -- Log (base 2) of (X+3) = 2.

Let’s use L2 as Log base 2
(2)(L2(x)) – L2(x+3)=2
The left side is
L2{x²/(x+3)}

Consider the right side of the equation.
2 is the L2 of some value
L2(a) = 2 mean that 2²=a therefore a=4 So antiL2(2) = 4

So, x²/(x+3)=4
x² = 4x+12
x² - 4x -12 = 0
(x+2)(x-6)=0
You can take it from there.

Answer 4

Remember:
"A logarithm is an index " (, is an exponent, is a logarithm).
So sum of logs (indices) corresponds to product of numbers (powers):
log a + log b = log (a * b) (same base); and
difference corresponds to quotient:
log a - log b = log (a / b) (same base); also,
multiple of log corresponds to log of power:
n * log a = log (a ^ n).

So here we have, starting with the RHS,
2 = log (x ^ 2) - log (x + 3) -- base 2 throughout
= log ((x ^ 2) / (x + 3))
Therefore 2 ^ 2 = (x ^ 2) / (x + 3);
so x ^ 2 = 4 (x + 3), = 4 x + 12 -- a simple quadratic equation easily solvable by standard methods, e.g., factors.
(Solutions are 6 and -2.)

Answer 5

Law of logs
log(x^2) - log(x+3) = 2
log[x^2 / (x+3)] = 2
x^2 / (x+3)] = 2^2 = 4
x^2 = 4x + 12
x^2 - 4x - 12 = 0

x = -2, 6

Answer 6

log(base 2) (x^2)-- log(base 2) (x+3)=2
log(base2) ((x^2)/(x+3))=2
2^2=(x^2)/(x+3)
4=(x^2)/(x+3)
4x+12=x^2
0=x^2-4x+12
0=(x-6)(x+2)
x=6,-2