logarithms , always true,sometimes true or never true , explain or give example
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log b^bn =n for any b>0
always true, b^n=b^n
log b^b =1 for any b>0
always true, because a number to the power of 1 always equals itself example: log4^4=1 ,4^1=4
log b^x is not a valid expression if x is a negative number
always true, becuase x is always a positive number so all powers if "a" will be positive
log b^1=0 for any base, b>0
always true, it id always zero example: logb^1=0. x^0=1
The value of log b^x is positive
sometimes true, VALUE of log b^x can also be negative but "b" and "x" are always positive