graphing functions and logs

Question

graph f(x)=2^x and g(x)=log2^x in the same rectangular coordiate system. show a table of values for each of the graphs. change g(x) log function to exponent form of the equation to find the values

Answer 1

Actual values on the graph are to a maximum of 3 decimal places accuracy.

x	2x	log10(2x)
-2	0.25 (¼)	-0.60
-1	0.5 (½)	-0.30
0	1	0
1	2	0.30

Values in the table are plotted to approximately 2 places of decimals.

The red graph is 2^x and is curved; the blue graph is log(2^x) (base 10) and is linear.

Let y=g(x)=log(2^x)=xlog(2)=0.301x approximately, which is linear. 10^g(x)=10^y=2^x is another way of expressing the function g.

Taking logs to base 2 we get: ylog₂(10)=x, and log₂(10)=1/log₁₀(2)=1/0.30103=3.32193 approx.