Beelog 2.0

Posted on by

Downie 3.7.9 cr2. How to wake up 2.0: Open eyes, put on decent clothes, open door, enjoy Various sunrise shots After getting back from taking some sunrise shots, I saw a man picking up the broken glass from about 6 beer bottles thrown around the night before by some inconsiderate (among other descriptive words) people. Mar 28, 2016 As you could have probably guessed from my title, this blog will take me home. I don’t mean Brisbane, it won’t get me there. But it will get me to the place that fills my lungs, eyes, ears and heart with home. Lightworks 12.6.rc1 software. I left off last time in my home state of NSW, but that was the southern side of the state and an unfamiliar city.

Algebra -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve for x: 2^logx= 1/4 Log On

Bee Log 2.0 For Sale


Question 448377: solve for x:
2^logx= 1/4
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
If you have a problem in which a variable appears in an exponent, one of the things to consider is taking a logarithm of both sides. This problem is:
2^(logx) = 1/4
Since the variable x is in the exponent, take the log of both sides:
log[2^(logx)] = log(1/4)
One of the properties of logarithms is that exponents come out as multipliers. This rule applies to the left side of this equation. Converting the exponent (log 2x) to a multiplier makes the equation become:
log(2)*logx = log(1/4)
Note that log(2) and log(1/4) are just numbers that can be found using a calculator. Log(2) = 0.301029995 and log(1/4) = log(0.25) = -0.602059991
Substituting these for log(2) and log(1/4) makes the equation become:
(0.301029995)*logx = -0.602059991
Divide both sides of this equation by 0.301029995 and the equation reduces to:
logx = -2
Ten is the base of the term 'log'. By definition 'if log to the base 10 of x equals y this is equivalent to saying the base 10 raised to the exponent y equals x.' Think of this and become familiar with this form of conversion.
As this definition applies to the equation:
logx = -2
We can say that 10 (the base) raised to the exponent -2 equals x. In equation form this is:
x = 10^(-2)
But by the rules of exponents 10^(-2) = 1/(10^2) = 1/100 = 0.01
This results in the answer:
x = 0.01
You can check this by substituting 0.01 for x in the original problem:
2^(log(x))
Substituting 0.01 for x:
2^(log(0.01))
Use a calculator to find that the log(0.01) = -2
So our term above becomes:
2^(-2)
By the rules of exponents, a negative exponent is equivalent to 1 over the term with a positive exponent. So this becomes:
2^(-2) = 1/[2^2) = 1/4
and this is exactly as the original problem statement said it should be.
When x equals 0.01, the term 2^logx does equal 1/4 or 0.25
Hope this helps you to understand the problem and how to think your way through it.

Bee Log Elementary