exponentials and logarithms: please help i never understood this and its my last test

[idontgetit]

how would i solve these problems (these aren't the actual problems from my test)
1.
a. 6^3x=100
b. log 2 + log(3x-1) = 10

2. given f(x)=log₂ (x-2)+3
find its domain, range, and the equation of its asymptote.


i remember using the saying...log b^a=y
is
b^y=a
so to solve number one i changed it to 6¹⁰⁰=3x am i on the right track?

 

[tkhunny]

These are the rules

1) log(ab) = log(a) + log(b) for suitable a and b

2) log(a/b) = log(a) / log(b) for suitable a and b

3) log(a^b) = b*log(a) for suitable a and b

4) \(\displaystyle \log_{b}(a) = c \iff b^{c} = a\)

Faced with this:

a. 6^3x=100

Introduce the base 10 logarithm

\(\displaystyle log(6^{3x}) = log(100)\)

Apply principle #3

3xlog(6) = log(100)

A little algebra and principle #3 again.

3xlog(6) = log(10^2) = 2log(10) = 2

A little algebra

x = 2/(3log(6))

See what you need for the other one!