kurrienewt kurrienewt
  • 12-01-2016
  • Mathematics
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3^b=17 exponentials into log form

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Willchemistry
Willchemistry Willchemistry
  • 12-01-2016
Solve for the real domain

[tex]3^b = 17[/tex]

if  f(x) = g(x) , then ln (f(x)) =  ln (g(x))

[tex]ln ( 3^b) = ln (17)[/tex]

[tex]log _{a} (x^b) = b*log _{a} (x)[/tex]

[tex]ln(3^b) = bln(3)[/tex]

[tex]bln(3) = ln (17)[/tex]

Solve  [tex]bln(3) = ln (17)[/tex]

[tex]b = \frac{ln(17)}{ln(3)} [/tex]

hope this helps !.
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