Question

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

Answer 1

is this log base 3 or log base ten?

Answer 2

base is 3

Answer 3

oops

Answer 4

so it is \[log_3(x-1)+log_3(x+25)=3\]?

Answer 5

yes

Answer 6

sorry i mistyped

Answer 7

if so then combine in to one logarithm using the property of logs:
\[log(A)+log(B) = log(AB)\]
\[log_3(x-1)(x+25)=3\]

Answer 8

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

Answer 9

let me know if any step is not clear.

Answer 10

its clear
I was just wondering why i got the -26 wrong, thanks for explaining why

Answer 11

welcome.