Write each expression in terms of common logarithms log4 304

Question

Write each expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).

Answer 1

Let x=log₄304, then 4^x=304;

log₁₀(4^x)=log₁₀(304), (common logs)

xlog₁₀(4)=log₁₀(304),

x=log₁₀(304)/log₁₀(4)=2.4829/0.6021=4.1240 approx. in decimal.