Common and Natural Logarithmic Functions?

Question

Translate the given logarithmic statement into an equivalent exponential statement.

1. log .001 = -3


Translate the given exponential statement into an equivalent logarithmic one.

2. 10^.4771 = 3

Please show the formulas and the ways you got the answer.

Show all work.

Thank you in advance

Answer 1

there is no formulas Just know that exp and log are inverse functions

10^(log .001)= 10 ^ -3
0.001 = 10 ^ (-3)

10^0.4771 = 3
log(10^0.4771) = log 3
0.4771 = log 3

Answer 2

when nothing is writen by the base of the log then the base is 10:
log .001 = -3 <--- so this log is base 10

use the log rule: log(base x) a =b
is like x^b=a

so in your case: log (base 10) .001= -3
is like 10^-3= .001
which is like: 10^-3 = 10^-3

this is true because when the power is negative the number becomes a fraction and so
10^-3 = 1/100 = .001

ithe same method is true for the other question as well log(base 10 )3= .4771
because 10^.4771 = 3

i hope this helped you :+)

Answer 3

taking a log, and raising to a power, are two "inverse" functions; that means each "undoes" the other. To put it more precisely:

10^(log(a)) = a

and:
log(10^a) = a

(assuming the base of the log is "10").

That means, generally, when you want to get rid of a "10^", you take the log of each side of the equation; and when you want to get rid of a "log", you raise 10 to each side of the equation.

> 1. log .001 = -3

Raise "10" to the value on each side of the equation:

10^(log .001) = 10^-3

On the left side, the "10^" undoes the "log", so:

.001 = 10^-3

> 2. 10^.4771 = 3

Take the log of each side of the equation:

log(10^.4771) = log(3)

The "log" undoes the "10^", so:

.4771 = log(3)

Answer 4

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Answer 5

1. 10^-3=.001

2. log(3)=.4771

Here is what I did: log(x) = y means 10^y=x