Hi,
Can anyone tell me if the following are correct please:-
If x = 10y (where x > 0), then log10 x = y
if a and b are positive numbers, then,
2 log 10 a / b = 2log 10 a - 2 log 10 b
and lastly
if a and b are positive numbers, then,
log 10 ( a+b ) = 10 log 10 a + log 10 b
Thanks.......
:-)
You have a typo in
"If x = 10y (where x > 0), then log10 x = y "
should say: If x = 10^y (where x > 0), then log10 x = y
the second one is right
the third one is wrong
log (a+b) cannot be split up
your answer of 10 log 10 a + log 10 b would be
log10[(a^10)(b)]
thank you
Hi! I'd be happy to help explain whether those statements are correct.
1. "If x = 10y (where x > 0), then log10 x = y": This statement is correct. In logarithmic terms, log10 x = y means that 10 raised to the power of y equals x. So if x = 10y, then log10 x = log10 (10y) = y.
2. "2 log 10 a / b = 2log 10 a - 2 log 10 b": This statement is incorrect. The correct statement is actually 2 log10 (a/b) = 2 log10 a - 2 log10 b. This is because when you divide two numbers inside a logarithm, it is equivalent to subtracting their logarithms. So, 2 log10 (a/b) = 2 (log10 a - log10 b) = 2 log10 a - 2 log10 b.
3. "log10 (a+b) = 10 log10 a + log10 b": This statement is also incorrect. The correct statement should be log10 (a+b) = log10 a + log10 b. When adding numbers inside a logarithm, it is equivalent to multiplying their values. So, log10 (a+b) = log10 (a * b) = log10 a + log10 b.
I hope this helps clarify the correctness of the statements. Let me know if you have any further questions!