Question

Hey anybody up for a log question?

Answer 1

@iGreen

Answer 2

Given the exponential equation 3x = 27, what is the logarithmic form of the equation in base 10?

Answer 3

Anybody?

Answer 4

3^x = 27 that is

Answer 5

for the log in standard form i got log base 3 of 27 = x

Answer 6

I just need to know how to get it into log form in base 10

Answer 7

PLEASE HELP

Answer 8

@mathstudent55

Answer 9

@phi

Answer 10

ok wat do u need

Answer 11

log3 (27) = x

Answer 12

like that

Answer 13

@twistnflip

Answer 14

I figured it out- I went back in the lesson the answer was:
(log base 10 of 27)/(log base 10 of 3)

Answer 15

I assume you know this, but we could have figured it out this way:
we know 10 to *some* power (call it y) must equal 3:
10^y =3
or, writing this equation using log base 10:
\[ \log_{10} 3 = y \]
(usually, if we just see "log" we assume base 10, so we could write it
\[ \log 3 = y\]

and using that value for y we can say
\[ 10^y =3 \\ 10^{ \log_{10} 3}= 3 \]
which is a bit complicated, but hopefully makes sense

now we use that "messy" vesion for 3 in
\[ 3^x = 27 \]
i.e., we can write
\[ \left( 10^{ \log_{10} 3}\right)^x= 27 \]

Answer 16

next, we use the property
\[ \left(a^b\right)^c = a^{bc} \]
to write
\[ \left( 10^{ \log_{10} 3}\right)^x= 27 \]
as
\[ 10^{x \log_{10} 3} = 27 \]
next, take the log (base 10) of both sides
\[ \log\left( 10^{x \log_{10} 3}\right) = \log(27) \]
the log "undoes" the exponent, so the left side becomes
\[ x \log 3 = \log(27) \]
finally, divide both sides by log3 (which is just a number , though a bit ugly)
\[ x= \frac{ \log 27}{\log 3} \]