Simplify:
Note: The first letters next to log are the small letters.
16.) logr r
17.) logt t^4
18.) logb 1
16.) logr r
r^? = r
? = 1
17.) logt t^4t^? = t^4
? = 4
18.) logb 1
b^? = 1
b = 0
(Any number to the zero power is one)
Thanks
Please forgive my sloppy typing. Here is what I meant. I hope you were able to figure it out anyway:
17.) logt t^4
t^? = t^4
? = 4
18.) logb 1
b^? = 1
? = 0
To simplify logarithmic expressions, you can use the following logarithmic identity:
logb(b) = 1
Using this identity, let's simplify each expression one by one.
16) logr r
Since the base of the logarithm (r) is the same as the argument of the logarithm (r), the expression simplifies to 1.
Answer: 1
17) logt t^4
Here, the base of the logarithm (t) is the same as the base of the argument of the logarithm (t^4). According to the power rule of logarithms, we can rewrite the expression as:
logt (t^4) = 4
Answer: 4
18) logb 1
In this case, the argument of the logarithm is 1. According to the logarithmic identity mentioned above, any logarithm with a base and argument of 1 will always be zero.
Answer: 0