logarithms without a base of 10?

Question

can someone please explain to me how to do logs w/o a base of ten and without it being an equation?

Is it just make it in exponential form?

For example if I have: Log(base 3) 4 does that equal 3^4 ? 81?

Thanks

Answer 1

log(base3)4=x

3^x=4
solve it

Answer 2

Log(base 3) 4 means: what is the power that if I raise 3 to do I get 4? So if Log(base3) 4 = x, then 3 to the power x = 4. An easier example would be Log (base2) 8 = 3 because 2 to the power 3 = 8.

Hope this helps.

Answer 3

log (base 3) 4 = x if 3^x = 4, so no, log (base 3) 4 does not equal 81, but log (base 3) 81 = 4.

Answer 4

log (base 10) of 100 = 2 or 10^2 =100
Likewise log (base 3) of 27 =3 or 3^3 = 27
Log (base 3) of 4 = x, means 3^x = 4

In the last example, you would find x by taking log of both sides:
log 3^x = log 4
xlog 3 = log 4
x= (log 4)/log 3

Answer 5

"if I have: Log(base 3) 4 does that equal 3^4 ? 81?"
No. If log₃x = 4, then x = 3^4. Got it?
log₃4 = ln 4/ln 3 = 1.26186

Answer 6

To solve problems like yours, i.e.
log[base 3](4)

You use what is called the "Change of Base" formula, and it goes as follows:

log [base c](a) = log[base b](a) / log[base b](c)

This means we can choose ANY base b. In this case, since our calculator is base 10 or base e friendly, we want to use one of those two bases. In our case,

log[base 3](4) = log[base b](4) / log[base b](3)

Choosing base 10:

log[base 3](4) = log(4) / log(3)

Choosing base 3:

log[base 3](4) = ln(4) / ln(3)

Both answers should give you the same result. This isn't something that's possible to do by hand, which is why you'd use your calculator to get the approximation.

Answer 7

this needs the change of base formula which is:

log (base x) y = log (base 10) y / log (base 10) x

so log (base 3) 4 = log 4 / log 3
Put that in your calculator and solve.

Answer 8

3 raised to what power gives you 4?
That's what log[3] (4) is equal to which is approximately 1.26.
3 is the base; so 3^1.26=4

Answer 9

The only bases in normal use are 10 & e. Other bases are used for highschool algebra classes.

log_3 4=x
4=3^x
ln 4 =x ln 3
x=ln 4/ln 3=1.261

log_3 4=1.261

Answer 10

n^(3/4) = 8 for the clarification that 8 = 2^3 n^(3/4) = 2^(3/a million) canceling the ^3... i.e.. taking the cube root of the two sides n^(a million/4) = 2 raising the two sides to the 4th ability n = 2^4 = 2x2x2x2 = 4x4 = sixteen

Answer 11

ok

now look at this fomula : log( base a) b = c

it means a^c =b

that's all.

so if you have log3 of 4 so you will have xroot of 4 equal to 3.