Log Graphs Quick Question

[Scremin34Egl]

Given the graph f(x) = log2^x and h(x) = 2^x

1.1) for what values of x is log2^x < -1

Which of these is correct?, x<1/2 or is this correct, 0<x<1/2

and some help with this

1.2) if g(x) = (100)*3^x, determine the value of x for which h(x) = g(x)

2^x = 100*3^x
2^x = 300^x...........stuck

 

[stapel]

Given the graph f(x) = log2^x and h(x) = 2^x

1.1) for what values of x is log2^x < -1

Which of these is correct?, x<1/2 or is this correct, 0<x<1/2

What are you seeing on the graph?

1.2) if g(x) = (100)*3^x, determine the value of x for which h(x) = g(x)

2^x = 100*3^x
2^x = 300^x...........stuck

Um... no. :shock:

It is not true that (100^1)*(3^x) equals (100^x)*(3^x) = (100*3)^x. Try instead to solve this exponential equation by using logs. If you take the log of each side, what do you get? Can you get the two variable-containing terms together on one side of the "equals" sign, with the remaining term on the other? What can you do next? And so forth.

 

[Bob Brown MSEE]

Given the graph f(x) = log2^x and h(x) = 2^x

1.1) for what values of x is log2^x < -1

Which of these is correct?, x<1/2 or is this correct, 0<x<1/2

x<1/2 for all defined values,
however f(x) is not defined for 0>x

so correct answer is 0<x<1/2

 

[Scremin34Egl]

Um... no. :shock:

It is not true that (100^1)*(3^x) equals (100^x)*(3^x) = (100*3)^x. Try instead to solve this exponential equation by using logs. If you take the log of each side, what do you get? Can you get the two variable-containing terms together on one side of the "equals" sign, with the remaining term on the other? What can you do next? And so forth.

A bit confused , maybe divide by 100 on both sides

 

[stapel]

A bit confused

Maybe you could follow the link in the reply which provides a lesson you can use to refresh on this topic...?

maybe divide by 100 on both sides

Maybe you could start by following the first step provided in the reply...?