Question 211501
logb w^2x/y^3z
-----
I believe this is meant to be:
{{{log(b,w^2*x/y^3*z)}}}
-----
That is the equation I am working with.
-----
The logarithmic properties we will be using are:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^c) = c*log(a)
-----
your equation is broken up into parts that can be converted to log form easy.
I made it look like this:
(w^2) * x * z / (y^3)
-----
We will take the log to the base b of this expression as is.
-----
we get:
{{{log(b,((w^2)*x*z / (y^3)))}}}
-----
First we'll separate out the individual entities I created.
The equation becomes:
{{{log(b,((w^2)*x*z / (y^3)))}}} = {{{log(b,(w^2)) + log(b,(x)) + log(b,(z)) - log(b,(y^3))}}}
-----
Next we'll take care of the exponent entries.
{{{log(b,((w^2)*x*z / (y^3)))}}} = {{{log(b,(w^2)) + log(b,(x)) + log(b,(z)) - log(b,(y^3))}}} becomes:
{{{log(b,((w^2)*x*z / (y^3)))}}} = {{{2*(log(b,(w))) + log(b,(x)) + log(b,(z)) - 3*(log(b,(y)))}}}
-----
To prove your answer is correct, you give some values to your variables and you solve using the original equation and you solve using the final equation.
-----
If you get the same answer, then that's a good indication that you did it right.
-----
I verified they are the same.
I used:
base = 10 (calculator can handle that)
w = 5
x = 3
y = 4
z = 2
-----
make sure you keep the exponents and roots intact (roots are just another form of exponents) until after you have separated all the multiplies and divides.
that's why I made them separate entities by enclosing them in parentheses.
-----