is log_2 ⁡4+log_2⁡ 8 = 5 true or false and why?

Question

i just want to know if this equation is true or false and why is, like how do the numbers add up to make it equal 5 or is it false and if it is how could you tell?

Answer 1

Hi Jaz! I think you'll find this question to be a bit simpler when you know this property:

"When adding log functions with the same base b, then log_b(x) + log_b(y) = log_b(xy)."

Since both log functions have a base of 2, then log₂(4) + log₂(8) is equal to log₂(32).

Knowing how logs function, we know that if log₂(32) = 5, then 2⁵ = 32. This is indeed true.

Hope this helps!