Logarithms

Question 1

y = logax is equal to

Answer 1

x=a^y

Question 2

So log5(125)=3 is equal to

Answer 2

125 = 5^3

Question 3

When adding logarithms with the same bass

Answer 3

The terms will be multiplied

Question 4

Log5(2) + log5(4) =

Answer 4

Log5(8)

Question 5

When taking away logarithms with the same bases

Answer 5

The terms will be divided (one taken away will be denominator)

Question 6

Log5(8) - Log5(2) =

Answer 6

Log5(4)

Question 7

Loga(x)^n=

Answer 7

nLoga(x)

Question 8

Loga(1)=

Answer 8

0 since a^0=1

Question 9

Loga(a) =

Answer 9

1 since a^1=a

Question 10

Solving equations with unknown components

Answer 10

Take loge of both sides and calculate accordingly

Question 11

e^x=7

Answer 11

loge(e)^x=loge(7)
x *1 = loge(7)
x=1.946

Question 12

Graphing with logarithmic axis, y=ab^x

Answer 12

Take logs of both sides so (log will be whatever is in question) so (loge for example)loge(y)=loge(ab^x)
Then use log rules to get it to loge(y) = loge(b)*x +loge(a)
Now use y = mx + c equation to show what m = loge(b) and c = Loge(a) now solve both for a and b and put them into y =ab^x equation

Question 13

Graphing with logarithmic axis, y=ax^b

Answer 13

Take logs of both sides (log will be whatever it is in question) so (loge for example)
Loge(y) =loge(ax^b)
Now solve using log rules to get Loge(y) = b*loge(x) + loge(a)
Now put y =mx +c equation below to show m=b and c = loge(a).
Solve both then find b and a, put these into original equation