Question

log3(3.3)=?

Answer 1

Rewrite in exponential notation.

\[3^{x} = 3.3\]

Take the log of both sides.

\[\log_{}3^{x} = \log_{} 3.3\]

Answer 2

Solve for x.

\[x \log_{} 3 = \log_{}3.3\]

Answer 3

ok

Answer 4

so what is its answer?

Answer 5

I already gave it to you. Just solve for x. You just have to divide both sides by log(3)

Answer 6

3= 3?

Answer 7

No.

x = log(3.3) / log(3)

Answer 8

x=3

Answer 9

That is the answer.

Answer 10

but its result is 1.087

Answer 11

Right.

If you take 3^(1.087) it should equal 3.3

Answer 12

ok

Answer 13

think what you need here is the almighty change of base formula. use
\[\log_b(A)=\frac{\log(A)}{\log(b)}\] so use
\[\frac{\log(3.3)}{\log(3)}\]

Answer 14

Same result.

Answer 15

yes but without exponentiating and then taking the log again.

Answer 16

If you don't like memorizing formulas, you can use definitions of what logs and exponentials are.

Answer 17

ok

Answer 18

point is that all logs are the same, in other words to solve
\[b^x=A\] for x you go right to
\[x=\frac{\ln(A)}{\ln(b)}=\frac{\log(A)}{\log(b)}\]

Answer 19

is it formular?

Answer 20

all logs are the same. they only differ by a constant. so you can use any one you like

Answer 21

in practice however, you only have two on your calculator, log base ten written as
log
and log base e written as
ln
so as a practical matter you use one of those

Answer 22

but i don't understand how you have its result is 1.087

Answer 23

well you do not know what power to raise 3 to in order to get 3.3
that is what you are looking for and why you need a calculator

Answer 24

That's what the definitions of a log is.

\[\log_{3}3.3 = 1.087 means 3^{1.087} = 3.3 \]

Answer 25

so you take out the calculator and type in
\[\log(3.3)\div \log(3)\] to get your answer

Answer 26

or you can type in
\[\ln(3.3)\div \ln(3)\] either way

Answer 27

what is mean In?