anonymous
  • anonymous
log3^(x-1)+log3^(x+25)=3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
is this log base 3 or log base ten?
anonymous
  • anonymous
base is 3
anonymous
  • anonymous
oops

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anonymous
  • anonymous
so it is \[log_3(x-1)+log_3(x+25)=3\]?
anonymous
  • anonymous
yes
anonymous
  • anonymous
sorry i mistyped
anonymous
  • anonymous
if so then combine in to one logarithm using the property of logs: \[log(A)+log(B) = log(AB)\] \[log_3(x-1)(x+25)=3\]
anonymous
  • anonymous
then write in equivalent exponential form to get \[(x-1)(x+25)=3^3=27\] \[x^2+24x-25=27\] \[x^2+24x-52=0\] \[(x-2)(x+26)=0\] \[x=2\] \[x=-26\] but -26 not a solution because you cannot take the log of a negative number, so answer should be 2
anonymous
  • anonymous
let me know if any step is not clear.
anonymous
  • anonymous
its clear I was just wondering why i got the -26 wrong, thanks for explaining why
anonymous
  • anonymous
welcome.

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