Question 13 of 25
1 answer:
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Answer: 6x
Work Shown:
For each step, the logs are all base b. This is to save time and hassle of writing tricky notation of having to write the smaller subscript 'b' multiple times. The first rule to use is that log(x^y) = y*log(x) for any base of a logarithm. The second rule is that meaning that the log base of itself is 1
log(b^(6x)) = 6x*log(b) .... pull down exponent using the first rule above
log(b^(6x)) = 6x*1 .... use the second rule mentioned
log(b^(6x)) = 6x
Answer:
y = 14
Step-by-step explanation:
For an exponential function of the form y = a
Use the given points to find a and b
Using (0, 14 ), then
14 = a (
= 1 ) , thus
a = 14
y = 14
Using (3, 3024 ) , then
3024 = 14 b³ ( divide both sides by 14 )
216 = b³ ( take the cube root of both sides )
b = = 6 , thus
y = 14 × ← exponential function