how to convert loge base a to the loga base 10?

Answer 1

There's a very easy way to convert from a logarithm in any base to a logarithm in any other base. The "base conversion formula" works like this: to convert from base a to base b,

log_b (x) = log_a (x) / log_a (b)

(Imagine that the _b and _a are little subscript b's and a's.)

In your case, you want to convert from base a to base 10, so we'll use the typical notation of "log" without a base to indicate base 10.

log x = log_a (x) / log_a (10)

In other words, to convert a log in any base to base 10, just divide by the log (base a) of 10.

Hope that helps!

Answer 2

log x to the base a
= log x to the base 10/log a to the base 10

Answer 3

Logb(x) = Loga(x)/Loga(b)

Here is why it works

If Loga(x) = A then x = a^A

and if Logb(x) = B then x = b^B

Now take logs to the base a of both sides to get

Loga(x) = B *Loga(b)

and so Loga(x) = Logb(x) * Loga(b)

rearrange to get Logb(x) = Loga(x) / Loga(b)

Answer 4

just follow simple fromula :

log to base e = 2.303 X log to base 10

Answer 5

There is no log e base a.

Answer 6

We have to calculate log(a)x = log(10)(?)

Let a^y=x, such that y=log(a)x

Now, log(a)x = [log(10)x]/[log(10)a]

Therefore, log(a)x = [log(10)x] * log(10)a