Question

what is the answer
log2 (4x)-log2 (x-5)= log2 8​

Answer 1

Answer:

1

Step-by-step explanation:

log2 will cancelled out and remain as

4x-x+5=8

3x=8-5

x=1

Answer 2

Step-by-step explanation:

Given:

$log_{2}(4x) - log_{2}(x - 5) = log_{2}(8)$

To find: Solve the logarithm equation.

Solution:

Tip:

$\bf log\left( \frac{x}{y} \right) = log(x) - log(y)$

Step 1: Apply the formula written in tip section.

$log_{2}(4x) - log_{2}(x - 5) = log_{2}(8)$

as

$log_{2} \left( \frac{4x}{x - 5} \right) = log_{2}(8)$

Step 2: Cancel log from both sides.

$\frac{4x}{x - 5} = 8$

Step 3: Cross multiply and solve for x.

$4x = 8(x - 5)$

or

$4x = 8x - 40$

or

$4x - 8x = - 40$

or

$- 4x = - 40$

or

$4x = 40$

or

$x = \frac{40}{4}$

or

$x = 10$

Final answer:

$\bf \red{x = 10}$

Hope it helps you.

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