Question 1187994
 1.

{{{1.7^x=49 }}}


 {{{log(1.7^x)=log(49) }}}


 {{{x*log(1.7)=log(49) }}}


{{{x*log(17/10)=log(7^2) }}}


{{{x*(log(17)-log(10))=2log(7) }}}


{{{x=2log(7) /(log(17)-log(10))}}}.......{{{log(10)=1}}}


{{{x=2log(7) /(log(17)-1)}}}


{{{x}}}≈{{{7.33436}}}



2.


{{{2.6^-3=(1/126) }}}=> assuming you have {{{2.6^(-3x)=(1/126) }}}


{{{2.6^(-3x)=(1/126) }}}.............{{{2.6^-3=(26/10)^-3=(13/5)^-3}}}


{{{(13/5)^(-3x)=(1/126) }}}


{{{log((13/5)^(-3x))=log((1/126)) }}}


{{{-3x*log(13/5)=log((1/126)) }}}


{{{-3x(log(13)-log(5))=log(1)-log(126) }}}........{{{log(1)=0}}}


{{{-3x(log(13)-log(5))=-log(126) }}}..............{{{2 log(3) + log(14) }}}


{{{-3x(log(13)-log(5))=-(2 log(3) + log(14)) }}}


{{{x=-(2 log(3) + log(14))/(-3(log(13)-log(5))) }}}


{{{x=-(2 log(3) + log(14))/(-3(log(13)-log(5))) }}}


 {{{x}}}≈{{{1.68715}}}


3.


{{{3.12^2=144}}} => assuming you have {{{3.12^(2x)=144}}}


{{{log(3.12^(2x))=log(144)}}}


{{{(2x)log(3.12)=log(12^2)}}}


{{{(2x)=(2log(12))/log(312/100)}}}


{{{(2x)=(2log(3*4))/(log(312)-log(100))}}}............{{{log(100)=2}}}, write {{{312=2^3*3*13}}}

{{{2x=(2log(3)+log(4))/(log(2^3*3*13)-2)}}}


{{{x=(2(log(3)+log(4)))/(2(3 log(2) + log(3) + log(13)-2))}}}


{{{x=(2(log(3)+log(4)))/(2(3 log(2) + log(3) + log(13)-2))}}}


{{{x = 2.18389}}}




1. 

{{{log(3 ,243)=log(3^5)/log(3)= 5log(3)/log(3)=5}}}

 2.
{{{log(6,(1/216) )=log(6, 1)-log(6,216) =0-log(6,6^3) =-3log(6,6)=-3*1=-3}}}

3.
{{{log(0.25, 16  )=log(16  )/log(0.25)=log(4^2  )/log(1/4)=(2log(4  ))/(log(1)-log(4))=(2log(4  ))/(0-log(4))=(2log(4  ))/(-log(4))=-2}}}