Logarithms

Question 1

What is the basic shape of a y=a^x graph?

Answer 1

• Passes through 0,1 and never goes negative.

- As a is closer the infinity the curve gets steeper.

Question 2

What is special about the y=e^x curve?

Answer 2

Y intercept of (0,2.71…) gradient function is the same.

Question 3

What is the interchangeable log formula?

Answer 3

Logab=c a^c=b

Question 4

What are the laws of logs?

Answer 4

logA+logB = logAB (the multiplication law)
log A − log B = log A (division law)
logAn =nlogA (power law).
-loga(x) = loga(1/x)

Question 5

What is important for the log laws?

Answer 5

they only work when the logs are of the same base and do not have a coefficient.

Question 6

What is the relationship between ln(x) and e^x?

Answer 6

They are reflections in the x axis.

Question 7

What is important at the end of solving a logarithm equation?

Answer 7

-At the end check if negative numbers as they will cause log error.

Question 8

How to solve equations with ln(x)?

How to solve equations with e^x?

Answer 8

• Raise both sides to e^ln(X)

- Ln both sides and then drop the x.

Question 9

What are the two ways linear graphs can be taken into logarithms?

Answer 9

-y=ax^b

or ab^x

Question 10

How could y=ax^b be turned into a log graph?

What is each component?

What are the two axes?

Answer 10

-log(y)=log(ax^b)
-log(y)=log(a)+log(x^b)
log(y)=log(a)+blog(x). = Y=MX+C

log(a) = c
blog(x)=MX
M=b

log(y) = y axis 
log(x)= x axis.

Question 11

How could y=ab^x be turned into a log graph?

What is each component of Y=MX+C

What are the axes?

Answer 11

-log(y)=log(ab^x)
-log(y)=log(a)+log(b^x)
log(y)=log(a)+xlog(b)

Y=MX+C
c= log(a)
MX=xlog(b)

Y axis = log(y)
X axis = x