4^u=324*9^u

Question

I need some help on this problem

Answer 1

4^u = 324*9^u

 

Divide both sides by 9^u:

 

4^u/9^u = 324

 

Take the log (I'll use the natural log, ln) of both sides:

 

ln(4^u/9^u) = ln(324)

 

Identity: ln(a/b) = lna - lnb:

 

ln(4^u) - ln(9^u) = ln(324)

 

Identity: ln(a^b) = bln(a):

 

uln(4) - uln(9) = ln(324)

u(ln(4) - ln(9)) = ln(324)

u = ln(324)/(ln(4)-ln(9)) ≅ -7.13

 

Answer 2

if you want to solve for U, then you need to know log or ln

 

first divide 9^u on both side

 

(4^u)/(9^u)=324

 

due to both have an exponent of u, it can bring the u out

 

(4/9)^u = 324

 

take a natural log (ln) on both side

 

ln[(4/9)^u] = ln(324)

 

bring the u down by the exponent rule of ln

 

u*ln(4/9) =ln(324)

 

divide ln(4/9) on both side

 

u = ln(324)/ln(4/9)

 

just plug that into a calculator to get the answer for u.