SOLUTION: Hello I'm confused on 2 of my homework problems; If the equation {{{ y=2^x }}} is graphed, which of the following values of x would produce a point closest to the x-axis? A.{{{ 1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello I'm confused on 2 of my homework problems; If the equation {{{ y=2^x }}} is graphed, which of the following values of x would produce a point closest to the x-axis? A.{{{ 1      Log On


   



Question 735892: Hello I'm confused on 2 of my homework problems;
If the equation +y=2%5Ex+ is graphed, which of the following values of x would produce a point closest to the x-axis? A.+1%2F4+ B. +3%2F4+ C. +5%2F3+ D. +8%2F3+
and
What is the value of +log%28+3%2C+27%29+?
Thanks.

Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Closest to the x-axis means the smallest
value of +y+.
The smallest value of +x+ will give you the
smallest value of +y+.
A. +1%2F4+ should be the right answer
---------------
+log%28+3%2C27+%29+
+log%28+3%2C3%5E3+%29+
This says +3%5Ex+=+3%5E3+
The answer is +3+




Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If the equation +y=2%5Ex+ is graphed, which of the following values of x would produce a point closest to the x-axis? A.+1%2F4+ B. +3%2F4+ C. +5%2F3+ D. +8%2F3+

+y=2%5Ex+....plug in given values

+y=2%5Ex+.....for +1%2F4+

+y=2%5E%281%2F4%29+
+y=root%284%2C2%29+
+highlight%28y=1.19%29+

+y=2%5Ex+.....for +3%2F4+

+y=2%5E%283%2F4%29+
+y=root%284%2C2%5E3%29+
+y=root%284%2C8%29+
+highlight%28y=1.68%29+

+y=2%5Ex+.....for +5%2F3+

+y=2%5E%285%2F3%29+
+y=root%283%2C2%5E5%29+
+highlight%28y=3.18%29+


+y=2%5Ex+.....for 8%2F3+

+y=2%5E%288%2F3%29+
+y=root%283%2C2%5E8%29+
+y=root%283%2C256%29+
+highlight%28y=6.35%29+
so, a point closest to the x-axis would be for A.+1%2F4+: (+1%2F4+,+1.19+)

see it on a graph:



2.
let the value of +log%28+3%2C+27%29+ be x
we are actually looking for x%5E3=27 ...solve for x
x=root%283%2C27%29
x=root%283%2C3%5E3%29
x=3
so, +log%28+3%2C+27%29=3+