SOLUTION: what is anti log of 4.567, 1.005869, 2.003 plz tell in stepwise form fast

Question 495222: what is anti log of 4.567, 1.005869, 2.003 plz tell in stepwise form fast

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the anti-log is the number who log is the number that you have.

some calculators can find it directly for you.

others make you work a little harder.

the basic equation of logarithms states:

y = log(b,x) if and only if b^y = x

b is equal to the base of the operation.

if you use the LOG function of your calculator, then b will be equal to 10.

assuming that's what you want to do, then:

y = log(10,x) if and only if 10^y = x

your first problem states:

log(x) = 4.567

the base of 10 is implied if it is not shown, so we will assume the base of the logarithm is 10.

from the basic law of logarithms that states:

y = log(x) if and only if 10^y = x, we can substitute for y to get:

4.567 = log(x) if and only if 10^4.567 = x

we can use our calculator to find that 10^4.567 = 36897.75986

your equation of y = log(x) becomes:

4.567 = log(36897.75986)

you can use your calculator to confirm that log(3687.75986) = 4.567

now that you know that you have to do, you should be able to solve the other 2 problems easier.

the second problem tells you:

log(x) = 1.005869

you know that y = log(x) if and only if 10^y = x

you know that y = 1.005869, so you get:

1.005869 = log(x) if and only if 10^1.005869 = x

this makes x equal to 10.13605597

you get:

1.005869 = log(10.13605597)

use your calculator to confirm.
it does.

your last problem is:

find anti-log of 2.003

now that you know the drill, you can immediately jump to 10^2.003 = 100.6931669

you get:

2.003 = log(x) becomes:
2.003 = log(100.6931669)

you can use your calculator to confirm by taking the log of 100.6931669 to get:
2.003 = 2.003
this confirms the answer is good.

the shortcut method is:
you want to find the anti-log of x.
you need to take 10^x and that is the anti-log.

this assumes you are looking for the anti-log to the base of 10.
the LOG function of your calculator assumes the base of 10.
any other base and it's a different story.

the general form is:

log(b,x) = y if and only if b^y = x
b is the base.
x is the number you want to get the log of.
y is the log of that number.

y is the log of a number x to the base b if and only if the base of b raised to the power of y is equal to the number x.

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