Relationship between exponentials & logarithms

Solve various problems that focus on the relationship between a^x=b and log_a(b)=x.

Problem

Table I contains outputs of the function f, left parenthesis, x, right parenthesis, equals, b, start superscript, x, end superscript for some x values, and Table II contains outputs of the function g, left parenthesis, x, right parenthesis, equals, log, start subscript, b, end subscript, left parenthesis, x, right parenthesis for some x values. In both functions, b is the same positive constant.
Fill in the missing values in the tables. If necessary, round your answer to three decimal places.
You do not need a calculator.
spaceTable I
xminus, 11, point, 04122, point, 041
b, start superscript, x, end superscript0, point, 111
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
110
spaceTable II
y0, point, 11011100
log, start subscript, b, end subscript, yminus, 11
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
2