Logarithm laws, step by step
log(5x) is log 5 + log x, log(x ÷ 5) is log x − log 5, and log(x⁵) is 5 log x.
The question
Check this line: log(x²) + log(x⁵) = 7 log x. Which is correct?
Check this line: log(x²) + log(x⁵) = 7 log x. Which is correct?
log(x²) + log(x⁵)
log(x²) + log(x⁵)=2 log x + 5 log x
log(x²) + log(x⁵)=2 log x + 5 log x
log(x²) + log(x⁵)=7 log x
log(x²) + log(x⁵)=7 log x
they wrote:7 log x
- Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
- On your own, and writing the step nobody writes down: log(x²) + log(x⁵) becomes 2 log x + 5 log x.
- Tidy that up and it is 7 log x.
- Now compare — and this time the two agree. The line on the page was already right, which is a finding, not a missing mistake. Some of them are.
How it works.
- 01
Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
- 02
On your own, and writing the step nobody writes down: log(x²) + log(x⁵) becomes 2 log x + 5 log x.
- 03
Tidy that up and it is 7 log x.
- 04
Now compare — and this time the two agree. The line on the page was already right, which is a finding, not a missing mistake. Some of them are.