When the logarithm is taken of any number to a power the result is that power times the log of the number; so taking logs of both sides gives:
e^x = 2
→ log(e^x) = log 2
→ x log e = log 2
Dividing both sides by log e gives:
x = (log 2)/(log e)
The value of the logarithm of the base when taken to that base is 1.
The logarithms can be taken to any base you like, however, if the base is e (natural logs, written as ln), then ln e = 1 which gives
x = (ln 2)/1 = ln 2
This is in fact the definition of a logarithm: the logarithm to a specific base of a number is the power of the base which equals that number.
In this case ln 2 is the number x such that e^x = 2.
----------------------------------------------------
This also means that you can calculate logs to any base if you can find logs to a specific base:
log (b^x) = y
→ x log b = log y
→ x = (log y)/(log b)
In other words, the log of a number to a given base, is the log of that number using any [second] base you like divided by the log of the base to the same [second] base.
eg log₂ 8 = ln 8 / ln 2 = 2.7094... / 0.6931... = 3
since log₂ 8 = 3 it means 2³ = 8 (which is true).
If e^x = 2 then taking logarithms to the base e, x = ln(2).
Solve the following equation for A : 2A/3 = 8 + 4A
5x+3 = x+4 5x-x = 4-3 4x = 1 x = 1/4 Thats not even close to how you solve it. First of all the equation is written 5^(x+3)=x+4. Simple Logarithms are needed to solve.
y=±√15
-4
x=-8
that is supposes to be 18 to the 6x power
It is not an equation if it does not have an equals sign. You could simplify it but not solve it.
a equals 5
I think it is 3.14 that equals to pi when u solve it
You cannot solve it since it is not a true equation.
Divide each side of the equation by 10 .
Solve the following equation for A : 2A/3 = 8 + 4A
You cant solve it unless it is an equation. To be an equation it must have an equals sign.
k equals 5.6
a=11
Easy! if -a = -4 then a = 4!!
Fsxjugfxbi