please give a detailed repsonse. thank you.
2007-08-28 15:12:28 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
10^x = 5
lg10^x = lg5
xlg10 = lg5
x = lg5 / lg10
x = lg5 / 1
x = 0.699 (to 3 sign fig)
2007-08-28 15:17:23 · answer #1 · answered by Kemmy 6 · 3⤊ 2⤋
Kemmy should get best answer
I just wanted to address the .5 thing
Anything to the .5 power is the square root. For example, 9^.5 == 3 . The square root of 10 would be a little over 3 (as 10 is closer to 9 than 16).
Also:
If you don't have a calculator or log tables, you can always "zero in"
10^(2/3) == (10^2)^(1/3) == 100^(1/3), which is very close to 5 (64^(1/3) is 4 and 125^(1/3) is 5).
That gives you a good starting point
So you know that the 2/3 ratio gives you an answer more than 4.5 (since 100 is closer to 125 than 64). You also know that you need to increase the numerator or decrease the denominator, since the answer is less than 5. If the answer was more than five, you would do the opposite.
Keep changing the ratio until you arrive at the answer you need (for example, I would try 3/4 next)
2007-08-28 15:43:40 · answer #2 · answered by Just Jess 7 · 0⤊ 0⤋
Log both sides
Log 10^x = Log 5
Log properties allow you to do this:
x log 10 = log 5
x = (log5 / log10)
You can figure out the values of log 5 and log 10 by using your calculator.
2007-08-28 15:18:04 · answer #3 · answered by Anonymous · 0⤊ 0⤋
take the log of each side of the equal sign
log (10^x) = log (5)
x log (10) = log (5)
x (1) = 0.69897
x is approximately equal to 0.7
2007-08-28 15:23:55 · answer #4 · answered by screaming monk 6 · 0⤊ 0⤋
kemmy has the best answer, don't listen to the people who say it's .5, because 10 to the .5 is 3.16, not 5
2007-08-28 15:20:00 · answer #5 · answered by J 2 · 0⤊ 0⤋
Take logarithms of both sides: x = Log(5)
Go to your friendly logarithm table and find the value of x for log(5) . Should be about 0.699
2007-08-28 15:18:27 · answer #6 · answered by cattbarf 7 · 1⤊ 1⤋
10^x = 5
you have to apply log to both sides having them as
log(10^x) = log(5)
by the rule of log, you can modify it to be
x * log10 = log 5
therefore
x = (log 5)/(log10)
2007-08-28 15:18:43 · answer #7 · answered by rawisamino 1 · 1⤊ 0⤋
you got to use Logs
so you just set it in logerthmic form or what ever it's called
log(Base 10)(5)=X
Log(5)=.69897
X=.69897
2007-08-28 15:18:28 · answer #8 · answered by Mr. Smith 5 · 1⤊ 0⤋
x is .5 because what it is saying is that 10 to the power of what equals 5. since your dividing 10 in half, ur multiplying by .5. hope that helps its kinda confusing.
2007-08-28 15:18:04 · answer #9 · answered by JUSTaPREPPYguy 4 · 1⤊ 4⤋
X has to be .5....Hmmmmmmmmmmm
10x.5=5.....Therefore X=.5?
2007-08-28 15:16:50 · answer #10 · answered by I Have Parasites 4 · 0⤊ 4⤋