graph y=logx, y=log(10x), and y=log(100x). how do the graphs compare? use a property of logs to show that the graphs are vertical shifts of one another.

There are a few different ideas you need to know here.

GRAPHING FUNCTION CONCEPTS

When graphing, y = f(x)...

*Stretch / Compression*

Replacing x with (ax) is a horizontal stretch/compression. y = f(ax)

Multiplying to get y = a*f(x) is a vertical stretch/compression.

You should also remember

For vertical moves, if a>1, the graph is stretching out vertically.

For horizontal moves, if a>1, the graph is compressing in horizontally.

*Shifts*

Replacing x with (x-b) is a horizontal shift. Moves entire graph left or right

y = f(x) + b is a vertical shift. Moves entire graph up or down

In this case function y= f(x) is y=logx.

PROPERTY OF LOGS

log

_{x}(a*b) = log_{x}(a)+log_{x}(b)When a base x is not shown, it is commonly assumed base x is 10.

log

_{10}(10^{a}) = a-----------------------------------------

OK so knowing all this, now we can start the problem... Wow.

y = logx AND y = log10x

y = log(10x), we are replacing x with 10x. x>1 Therefore, this is a

*horizontal compression*.y = log10x = log10 + logx

y = 1+logx

y = logx + 1 Therefore, this is

*vertical shift*of y = logx. The graph moves up 1.I know this is a lot of information, but if you take the time to understand all these ideas, you will likely be ahead of your class!