Is log8 (x/2) same as log8 x/2?

[wzwz]

Is log8 (x/2) same with log8 x/2?

 

[phinds]

Is log8 (x/2) same with log8 x/2?

Can you compute them and find out?

 

[fresh_42]

Depends on what is hidden behind this sloppy notation:
$$
\log (8 \cdot \dfrac{x}{2})\; , \; \log \dfrac{8x}{2} \; , \; \dfrac{x}{2} \cdot \log 8 \; , \; \log_8 \dfrac{x}{2} \; , \; \dfrac{1}{2}\cdot \log_8 x \; , \;\dfrac{1}{2}\cdot \log (8x) \; , \;\dfrac{1}{2}\cdot x \cdot \log 8
$$
Make your choice.

 

[Charles Link]

The order of operations is well defined for exponents, and multiplication, and addition, but how it works with the log function doesn't seem to be nearly so conventional. When in doubt, use parentheses. When I was a high school student studying algebra in 1972, I asked the teacher the same question, about the order of operations for the log function. He didn't know the answer, and/or didn't understand the question.

 

[Mark44]

Is log8 (x/2) same with log8 x/2?

To elaborate on what @fresh_42 said, what you wrote isn't clear. The second expression might be interpreted as $\frac{\log_8 x}{2}$, which is different from $\log_8 \frac x 2$.

 

[FactChecker]

Without parenthesis, I would read log8 x/2 as (log8 x)/2. Parenthesis are cheap. Use them.

 

[lekh2003]

Is log8 (x/2) same with log8 x/2?

First of all, use parentheses, everywhere. Even when they are redundant. Make it absolutely clear that no errors can be made if you follow the parentheses. Usually it doesn't matter much, but in this question, it is impossible to distinguish the bases from the actual values without proper parentheses and terms.

Instead of the forum helping you, just set x equal to anything and do what you think it is.

If you ever have to check a property in math, just set the variable equal to 1, and solve. It can be in logarithms, exponents, etc. Just make everything into simple numbers that can be calculated and check.