# Thread: two simple log questions

1. ## two simple log questions

Hi everyone, just need help with two little questions:

1. state as a single log in simplest form: $\displaystyle \frac{1}{2}log_{a}x - \frac{2}{3}log_{a}y$

isn't this just $\displaystyle log_{a}\frac{x^\frac{1}{2}}{y^\frac{2}{3}}$

2. solve for x in $\displaystyle 5^{x^2-x} = 7$

is there an easier way than changing it to a quadratic, setting to 0 and solving?

$\displaystyle 5^{x^2-x} = 7$

$\displaystyle (x^2-x)log5 = log7$

$\displaystyle x^2-x = \frac{log7}{log5}$

$\displaystyle x^2-x-\frac{log7}{log5} = 0$

2. Originally Posted by hello
Hi everyone, just need help with two little questions:

1. state as a single log in simplest form: $\displaystyle \frac{1}{2}log_{a}x - \frac{2}{3}log_{a}y$

isn't this just $\displaystyle log_{a}\frac{x^\frac{1}{2}}{y^\frac{2}{3}}$

2. solve for x in $\displaystyle 5^{x^2-x} = 7$

is there an easier way than changing it to a quadratic, setting to 0 and solving?

$\displaystyle 5^{x^2-x} = 7$

$\displaystyle (x^2-x)log5 = log7$

$\displaystyle x^2-x = \frac{log7}{log5}$

$\displaystyle x^2-x-\frac{log7}{log5} = 0$
1. Correct

2. No quicker way that I know of. Should be easy enough to solve using the quadratic formula