Question

how can I simpify the following (preferably, without using a calculator):

a) (3^3)/(squareRoot(3^5))

b) 4ln(squareRoot(x))+6ln(x^(1/3))

p.s. i use squareRoot() beacause i dont know how to write a root symbol.

Answer 1

Is this the correct form?
a) \[3^3 / \sqrt{3^5}\]

b) \[4 \ln \sqrt{x} + 6lnx^{1/3}\]

I won't be able to get back to you for a while, so sorry if I can't continue to help. But my advice for a) is to first convert the denominator into a form in which simplifying is simple. For b) remember your logarithmic identities, and combine the terms into a simplified logarithm; once again, remember your special rules with exponents (and logarithms!). Good luck!

Answer 2

Here are the rules:

For a)
\[x^{a}x ^{b}=x ^{a+b}\]
*remember you can rewrite a root as a fractional exponent, and a denominator as a negative exponent, for example:
\[\sqrt{x}=x ^{1/2}\]
\[1/\sqrt{x}=x ^{-1/2}\]

For b)
\[a \ln (x)=\ln (x ^{a})\]
and
\[\ln (a)+\ln (b)=\ln (ab)\]

Hope that helps!