Express as a single logarithm:

3 log(b) (3√x) - 2 log(b) (x)

9 log(b) (x) - 2 log(b) (x)
9/2 log(b) x

Is this the correct process?

Question

Express as a single logarithm:

3 log(b) (3√x) - 2 log(b) (x)

9 log(b) (x) - 2 log(b) (x)
9/2 log(b) x

Is this the correct process?

e.mccormick · Answer

Well, you did not take care of the exponent first, so...

anonymous · Answer

The cube root of x was multiplied to the coefficient?

e.mccormick · Answer

3 log(b) (3√x) - 2 log(b) (x) $\leftarrow$ the numbers out front.  What can they be shown as in a log?

anonymous · Answer

Exponents which means the first one could also be shown as:

log(b) (x)

Because it's the cube root of x, cubed?

e.mccormick · Answer

$(3\sqrt{x})^3=x$?

e.mccormick · Answer

Or is that the 3rd root?

anonymous · Answer

The cube root. It's just x. Thank you!

e.mccormick · Answer

Kk.

So you do that first, then you do the other log actions.

e.mccormick · Answer

And here is a nice reference on the basic rules, just in case: http://www.purplemath.com/modules/logrules.htm have fun!

anonymous · Answer

Thanks! Will do.