Question

What is the value in log 2(x)-3 = 1?

Answer 1

`x=16`

Explanation:

In this problem, we need to solve for the variable x in the equation:

`\log_2(x)-3=1`

First, we need to isolate the logarithm containing x on one side. We can do this by adding 3 to both sides.

`\log_2(x) = 4`

Next, we can raise both sides to the power of 2 to negate the logarithm.

`\displaystyle 2^(\log_2(x)) = 2^4`

This simplifies nicely to:

`x = 2^4`

Finally, we can evaluate the exponent on the right side.

`\boxed{x = 16}`

Further Note

A logarithmic function outputs the number that the base (in this case, 2) must be raised to in order for it to have the same value as the expression inside the function. For example:

`\displaystyle \log_2\!\left(2^4\right) = 4`