Evaluating Logarithms using the Change of Base Formula
Use the change of base formula to rewrite the logarithm using base 10 logarithms. Then use your calculator to evaluate the logarithm. Round your result to three decimal places.
Logarithmic FunctionRewritten using the change of base formulaEvaluated using the calculator
f(x)=log⁡2(x)\displaystyle {f{{\left({x}\right)}}}={{\log}_{{2}}{\left({x}\right)}}f(8)=log⁡2(8)=log⁡(8)log⁡(2)\displaystyle {f{{\left({8}\right)}}}={{\log}_{{2}}{\left({8}\right)}}=\frac{{\log{{\left({8}\right)}}}}{{\log{{\left({2}\right)}}}}f(8)=3\displaystyle {f{{\left({8}\right)}}}={3}
f(x)=log⁡6(x)\displaystyle {f{{\left({x}\right)}}}={{\log}_{{6}}{\left({x}\right)}}
f(101)=\displaystyle {f{{\left({101}\right)}}}=
 
  		=
 
 
f(101)=\displaystyle {f{{\left({101}\right)}}}=
g(x)=log⁡4(x)\displaystyle {g{{\left({x}\right)}}}={{\log}_{{4}}{\left({x}\right)}}
g(68)=\displaystyle {g{{\left({68}\right)}}}=
 
  		=
 
 
g(68)=\displaystyle {g{{\left({68}\right)}}}=
h(x)=log⁡3(x)\displaystyle {h}{\left({x}\right)}={{\log}_{{3}}{\left({x}\right)}}
h(122)=\displaystyle {h}{\left({122}\right)}=
 
  		=
 
 
f(122)=\displaystyle {f{{\left({122}\right)}}}=
p(t)=log⁡8(t)\displaystyle {p}{\left({t}\right)}={{\log}_{{8}}{\left({t}\right)}}
p(124)=\displaystyle {p}{\left({124}\right)}=
 
  		=
 
 
f(124)=\displaystyle {f{{\left({124}\right)}}}=
f(x)=log⁡5(x)\displaystyle {f{{\left({x}\right)}}}={{\log}_{{5}}{\left({x}\right)}}
f(46)=\displaystyle {f{{\left({46}\right)}}}=
 
  		=
 
 
f(46)=\displaystyle {f{{\left({46}\right)}}}=

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