SOLUTION: Evaluate the expression without using a calculator. log16 4

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Question 1180585: Evaluate the expression without using a calculator.
log16 4

Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%2816%2C%28+4%29%29..........convert to base 10

=log%28%28+4%29%29%2Flog%28%2816%29%29

=log%28%28+4%29%29%2Flog%28%284%5E2%29%29

=log%28%28+4%29%29%2F%282log%28%284%29%29%29

=cross%28log%28%28+4%29%29%291%2F%282cross%28log%28%284%29%29%29%29

=1%2F2


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Evaluate the expression without using a calculator.
log16 4
log16 (4)

  16x = 4 ----- Converting to EXPONENTIAL form

(42)x = 4

  42x = 41

   2x = 1 ----- Bases are equal, and so are the exponents