Question 483270
1. If possible evaluate g(t)for the given values of t
g(t)=2t^3 - t^2 + 4


you did not give any values of t so i wouldn't know how to answer question 1.
the procedure, however, would be the same as shown below:


equation g(t) = 2t^3 - t^2 + 4
solve for t = 3
the equation becomes:
g(3) = 2*(3)^3 - (3)^2 + 4
all you're doing is replacing t with 3 in the equation.
the answer, in that case, would be:
g(3) = 2*27 - 9 + 4 which becomes:
g(3) = 54 - 5 which becomes:
g(3) = 49



2. log(2,2^6)


you are looking to find the log of 2^6 to the base of 2.
since, in general, log(a^b) = b*log(a), your expression becomes:
6 * log(2,2)


to find 6 * log(2,2), you can use your calculator by converting the base of 2 to the base of 10 using the logarithm base conversion formula shown below.


6 * log(2,2) = 6 * ((log(10,2) / log(10,2))


the general formula is:


log(a,b) = log(c,b) / log(c,a)
a is the base you want to convert from.
c is the base you want to convert to.
b is the log value you are looking to solve for.
the expression of log of b to the base a is converted to:
log of b to the base c divided by log of a to the base c.


this allows you to use the LOG function of your calculator.


the formula becomes:


6 * log(2,2) = 6 * (LOG(2) / LOG(2)).


the answer is 6 * 1 because anything divided by itself is equal to 1.


your final answer is 6.


you would want to confirm your answer to make sure it's correct.
the basic definition of logs states:
y = log(b,x) if and only if b^y = x
your original expression is:
log(2,2^6)
set y equal to this to get:
y = log(2,2^6)
set x equal to 2^6 to get:
y = log(2,x)
set b equal to 2 to get:
y = log(b,x)
the basic definition of logarithms states that:
y = log(b,x) if and only if b^y = x
now, you know that b is equal to 2 and you know that x = 2^6, so this equation becomes:
2^y = 2^6
this equation is true if y = 6 because then you get:
2^6 = 2^6 which is true.
6 is the answer to your question.
log(2,2^6) = 6