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)
