log3^(x-1)+log3^(x+25)=3

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log3^(x-1)+log3^(x+25)=3

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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is this log base 3 or log base ten?
base is 3
oops

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so it is \[log_3(x-1)+log_3(x+25)=3\]?
yes
sorry i mistyped
if so then combine in to one logarithm using the property of logs: \[log(A)+log(B) = log(AB)\] \[log_3(x-1)(x+25)=3\]
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
let me know if any step is not clear.
its clear I was just wondering why i got the -26 wrong, thanks for explaining why
welcome.

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