Question

Solve the equation by using tu basic properties of logarithms log(2x)=3 (Picture provided)

Answer 1

Answer:

Option b

Step-by-step explanation:

According to the property of sum of logarithms we know that

$log(ab) = log(a) + log(b)$.

In this case we have the equation:

$log(2x) = 3$

Using the property of sum of logarithms:

$log(2) + log(x) = 3$

$log(x) = 3 - log(2)$

We also know that:

$10 ^{(logx)} = x$     -------- Inverse logarithm

So:

$x = 10 ^{3-log(2)}$

$x = 500$

Another easiest way to solve it is the following:

Make $w = 2x$.

Then:

$log(2x) = log(w)$

$log(w) = 3$

$w = 10^3$  -------- Inverse logarithm property

$w = 1000$  

but $w= 2x$. Then:

$2x = 1000\\\\x = 500$