Question

State the domain of the function y=log(2) 5x+4 no calc

Answer 1

\[\text {You mean } log_2(5x+4) \text{ right?} \]


Well in the case of logarithms the argument of the log has to be greater than zero (since no power of 2 gives a negative no.)

So, the argument, here, i.e. 5x+4, which should be greater than zero.

so,
5x+4 > 0
or, 5x > -4
or, x > -4/5

So, 'x' can assume any value which is greater than (-4/5).

Hence domain of x:

\[x \text{ }\epsilon \text{ } (\frac {-4} 5 ,\infty)\]