# Thread: I dont really understand this logarithmic rule...

1. ## I dont really understand this logarithmic rule...

question number 1:
a ^ (log x to the base a) = x
or

10 ^ (log x) = x

or

e ^ (lnx) = x

question number 2:
confused about the ln problem help!!!
Find x
ln5 + ln10 = lnx

kindly pls help me understand the two questions we have a test tommorow and i need to get perfect

question number 1:
a ^ (log x to the base a) = x
or

10 ^ (log x) = x

or

e ^ (lnx) = x

question number 2:
confused about the ln problem help!!!
Find x
ln5 + ln10 = lnx

kindly pls help me understand the two questions we have a test tommorow and i need to get perfect
The answer to your first problem is that a^ and "log to the base a" are inverse functions. So a^{log(a)x} = x and log(a)a^x = x by definition.

ln(5) + ln(10) = ln(x)

The sum of two logs multiplies the arguments, ie ln(a) + ln(b) = ln(ab), so

ln(5*10) = ln(x)

ln(50) = ln(x)

Thus x = 50.

-Dan

question number 2:
confused about the ln problem help!!!
Find x
ln5 + ln10 = lnx

kindly pls help me understand the two questions we have a test tommorow and i need to get perfect
Rules of logs:

log(x^y)=y*log(x)

and

log(xy)=log(x)+log(y)

therefore: ln5+ln10=ln(5*10)=ln50

so x equals 50.