Change the following to logarithmic or exponential form.
Note:
log_a c=b can be written as:
aᵇ=c
hence:
1. log₄ 16=2
will be written in exponential as:
4²=16
2. 25^(1/2)=5
will be written in logarithmic form as:
log₂₅5=1/2
3. Which function represents exponential growth?
#N/B For an exponential function:
y=a(b)^x
when b>1 it exponential growth
when b<1 it is an exponential decay
F: y=1/20(4)ˣ
b=4>1
exponential growth
G: y=16(0.4)ˣ
b=0.4<1
exponential decay
H: 20(1/8)ˣ
b=1/8<1
exponential decay
I. y=8x³
The above function does not have a growth factor, thus
it is a polynomial function not an exponential function.
4. Solve log₄3+log₄x=log₄18
when we add log functions we can multiply them as follows:
log₄(3*x)=log₄18
the log₄ will cancel and we shall remain with:
3x=18
solving for x we get:
(3x)/3=18/3
thus
x=6
5. Solve log₇36x-log₇2=log₇9
Dividing log functions is like subtracting them, thus we shall have:
log₇(36x/2)=log₇9
simplifying this we get:
log₇ 18x=log₇9
log₇ will cancel because of the same base and we shall have:
18x=9
thus
x=9/18
x=1/2
Expand the following:
Remember:
Multiplying logs is the same as adding them
Subtracting logs is the same as dividing them
thus
6. log₃ 4xy
expanding the above give us:
log₃4+log₃x+log₃y
Answer: log₃4+log₃x+log₃y
7. log₅ (xy²)/3
expanding this gives us:
log₅x+log₅y²-log₅3
Answer: log₅x+log₅y²-log₅3
Condense the following logarithms:
Using the concept from 6 and 7 we shall have:
8. log₈2+log₈7-log₈x
condensing this will give us:
log₈[(2*7)/x]
simplifying gives us:
log₈(14/x)
9. log₇9+3log₇y-4log₇2
Condensing the above gives us:
log₇9+3log₇y-4log₇2
=log₇9+log₇y³-4log₇2
=log₇(9*y³)/2
=log₇(9y³/2)
