What is the solution to log2(9x)-log2^3=3?

Question

asked Aug 3, 2018 90.2k views

2 Answers

Abbas Jafari · Answer 1 · 2018-08-08T19:56:24+0000

Answer:

x = (8)/(3) is the solution to
$\log_2 9x - \log_2 3 = 3$

Explanation:

Using the logarithmic rules:

$\log (m)/(n) = \log m -\log n$

if
$\log_b x = a$ then;

x = b^a

Given the equation:

$\log_2 9x - \log_2 3 = 3$

Solve for x:

Apply the logarithmic rules:

$\log_2 (9x)/(3) = 3$

⇒
$\log_2  3x = 3$

Apply the logarithmic rules;

3x = 2^3

⇒
3x = 8

Divide both sides by 3 we have;

x = (8)/(3)

Therefore, the solution for the given equations is,