1. Find $x$ if $\log_9(2x-7) = \dfrac{3}{2}$.
2. Calculate $\sqrt{10p} \cdot \sqrt{5p^2} \cdot \sqrt{6p^4}$ . Express your answer in simplest radical form in terms of $p$. Note: When entering a square root with more than one character, you must use parentheses or brackets. For example, you should enter $\sqrt{14}$ as "sqrt(14)" or "sqrt{14}".
3. Find all solutions $x$ of the inequality $$\frac{5}{24} + \left|x-\frac{11}{48}\right| < \frac{5}{16}.$$Express your answer in interval notation, simplifying all fractions in your answer.
+981 1. log9(2x-7)=1.5
logab = c means that ac = b
So this equation means that:
9 to the power of 1.5 is equal to (2x-7)
9^1.5 = 2x - 7
Since 9^1.5 = 27, 2x - 7 = 27
Solving for x, we have that x = 17.
+128474 \( \frac{5}{24} + \left|x-\frac{11}{48}\right| < \frac{5}{16}\)
subtract 5/24 from both sides
l x - 11/48 l < 5/16 - 5/24
l x - 11/48 l < 15/48 - 10/48
l x - 11/48 l < 5/48 we have two equations, here
x - 11/48 < 5/48 x - 11/48 > - 5/48
add 11/48 to both sides
x < 16/48 x > 6/48
x < 1/3 x > 1/8
x = ( 1/8 , 1/3)
