Logs & Exponentials
1. Find the value of x in each of the following:
a) x = log22 b) log2x = 5 c) -2 = log3x
2. Find the value of:
a) log381 b) log41 c) log5(
)
3. Simplify:
a) log105 + log1010 – log10(1/2)
b) log 5 + log 6 – log10 + log(1/3)
c) log39 – log3(1/3)
4 Solve for x:
a) log(x + 1) + log(x – 1) = log3
b) log5(x + 1) + log5(x – 3) = 1
c) 2log2x + log22 = 7

5.
Find the relationship between x and y.
6.

Find the relationship between x and y.
7. The population of a certain city is 80 000. Assuming that the growth is exponential, the population P after t years is given by:
P = 80 000(1.2)0.1t
a) Find the population after 20 years
b) How long does it take for the population to double?