How do you solve 2094n=5?

2 Answers
Jul 20, 2017

n=9log2054

Explanation:

We know that :

xy=zy=logxz

so :

2094n=594n=log2054n=9log205

n=9log2054

Jul 20, 2017

n=9414(log5log20)

n=2.116

Explanation:

In a question like this you first have to decide whether you will solve it as an exponential equation, or use logs.

5 is certainly not a power of 20, so logs are indicated.

2094n=5 find log of both sides

log2094n=log5 apply the power law

(94n)log20=log5 isolate the factor with n

94n=log5log20 re-arrange to get 4n positive

9log5log20=4n divide by 4

14(9log5log20)=n

n=9414(log5log20)

n=2.116 (to 3 d.p.)