shakyasundari5
Answered

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If 2^a =3,5^b = 2 and abc=1 find the value of 3^c

Sagot :

dashataran

Solution:

[tex]\text{First take the logarithm on both sides of the equation $2^a=3:$}[/tex]

      [tex]\log(2^a)=\log3[/tex]

[tex]\text{Recall: $\boxed{\log_wx^y=y.\log_wx}$}[/tex]

      [tex]a.\log2=\log3[/tex]

      [tex]a=\dfrac{\log3}{\log2}[/tex]

[tex]\text{Next, take the logarithm on both sides of the equation $5^b=2:$}[/tex]

      [tex]b.\log5=\log2\\[/tex]

      [tex]b=\dfrac{\log2}{\log5}[/tex]

[tex]\text{Solve for $c$ in $abc=1:$}[/tex]

      [tex]abc=1[/tex]

      [tex]\dfrac{\log3}{\log2}\times\dfrac{\log2}{\log5}\times c=1[/tex]

      [tex]c.\log3=\log5[/tex]

      [tex]\log3^c=\log5[/tex]

      [tex]\boxed{3^c=5}[/tex]

     

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