Two more logarithm questions!

[siobhanfowler]

Solve for x in the following equation:
log[sub:232qava0]7[/sub:232qava0]x + log[sub:232qava0]7[/sub:232qava0](x - 1) = log[sub:232qava0]7[/sub:232qava0]2x

And these questions I answered, but I am not sure if I have done so correctly.

Beginning with the function f(x)=log[sub:232qava0]a[/sub:232qava0]x , state what transofrmations were used on this to obtain the functions given below:

p(x)= -[sup:232qava0]5/8[/sup:232qava0]log[sub:232qava0]a[/sub:232qava0]x
- A vertical compression by 5/8, and relfected in the x-axis.

r(x)= log[sub:232qava0]a[/sub:232qava0](5-x)
- Transformed horizonatally 5 right.

t(x)= 2log[sub:232qava0]a[/sub:232qava0]2x
- I know this is a vertical stretch by 2, but I am not sure how the 2x at the end affects the graph.

Oops! I lied! One more question!

Is log[sub:232qava0]3[/sub:232qava0]5 equal to log[sub:232qava0]5[/sub:232qava0]3 ? Evaluate without using logarithms.

 

[tkhunny]

You MUST show your work. Really.

You need this, log(a) + log(b) = log(a*b)

You need this, If \(\displaystyle log_{a}(b) = c\), then \(\displaystyle a^{c} = b\)

Let's see what you get.

 

[mmm4444bot]

log[sub:3prh9g52]7[/sub:3prh9g52]x + log[sub:3prh9g52]7[/sub:3prh9g52](x - 1) = log[sub:3prh9g52]7[/sub:3prh9g52]2x

Use the property posted by tkhunny to rewrite the lefthand side.

Then equate the logarithms' arguments, to form a quadratic equation in x.

Check your solution candidates.


p(x)= -[sup:3prh9g52]5/8[/sup:3prh9g52]log[sub:3prh9g52]a[/sub:3prh9g52]x
- A vertical compression by 5/8, and relfected in the x-axis.

I agree.


r(x)= log[sub:3prh9g52]a[/sub:3prh9g52](5-x)
- Transformed horizonatally 5 right.

This is not correct.

If the argument were to be (x - 5), instead, then the graph would be shifted five units to the right.


t(x)= 2log[sub:3prh9g52]a[/sub:3prh9g52]2x
- I know this is a vertical stretch by 2, but I am not sure how the 2x at the end affects the graph.

Review your class materials for transformations of the type f(k*x).


Is log[sub:3prh9g52]3[/sub:3prh9g52]5 equal to log[sub:3prh9g52]5[/sub:3prh9g52]3 ? Evaluate without using logarithms.

tkhunny suggested that you consider exponential form.

Another approach would be to apply the Change-of-Base formula (if you've learned it).

In other words, is it possible for the following equation to hold true?

log(5)/log(3) = log(3)/log(5)