I don't get the hate. Yes, easy to do in your head, but understanding the approaches can assist on harder similar problems and is a good way to see how some of the exponential properties apply easily.
This simple problem is a good starting point to show early learners how to apply the properties of exponents to solve certain classes of equations. After they have that under their belt, *then* step it up with related problems that require the longer, more tedious approach used here. And I don't think that it's "hate"; but, as someone who has taught math, I think that jumping right into this unnecessary level of detail will turn away most of the people whom you want to help.
That was certainly a round-about (and confusing) approach.
It simple. Like 6 * 4 is really (3 * 2) * (2 * 2), which of course is 2(3 * 2), which is 2 * 6....
ya know, just use a calculator.
Took about 5 seconds to know it's 5/3 ... Log2(32)/Log2(8)
2 cubed to power of x is 32. 2 to the power of 5 is 32. so 8 to the power of 5/3 is 32 - no need for logs just basic laws of indices
I've got a better solution: 2^3x = 2^5 therefor 3x = 5 and x = 5/3
Exactly! Takes about 5 seconds.
That's more like it .
exactly
I was able to solve it by inspection in about 5 seconds.
At what point of obviousness is it acceptable on a test to just give the answer?
I don't get the hate. Yes, easy to do in your head, but understanding the approaches can assist on harder similar problems and is a good way to see how some of the exponential properties apply easily.
This simple problem is a good starting point to show early learners how to apply the properties of exponents to solve certain classes of equations. After they have that under their belt, *then* step it up with related problems that require the longer, more tedious approach used here.
And I don't think that it's "hate"; but, as someone who has taught math, I think that jumping right into this unnecessary level of detail will turn away most of the people whom you want to help.