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Solve exponential equations using logarithms: base-10 and base-e

Consider the equation 14⋅100.5w=10014\cdot 10^{\large{0.5w}}=100.
Solve the equation for ww. Express the solution as a logarithm in base-1010.
w=w=
Approximate the value of ww. Round your answer to the nearest thousandth.
w≈w\approx
  • Your answer should be
  • an integer, like 66
  • an exact decimal, like 0.750.75
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4