Question 174941
Let {{{x=log(10,(m))}}} Note: if the base is not stated, the default base is 10



So we go from {{{2*log(10,(m))+3*log(10,(m))=10}}} to {{{2x+3x=10}}}



{{{2x+3x=10}}} Start with the given equation.



{{{5x=10}}} Combine like terms on the left side.



{{{x=(10)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.



{{{x=2}}} Reduce.



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{{{log(10,(m))=2}}} Plug in {{{x=log(10,(m))}}}



{{{10^2=m}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{100=m}}} Square 10 to get 100



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Answer:



So the solution is {{{m=100}}}