Question

solve the following equation ( i want with steps)
log(x-5) = 1-log(x-14)

Answer 1

start with
\[\log(x-5)+\log(x-14)=1\]
then using a property of the log write
\[\log((x-5)(x-14))=1\]

Answer 2

rewrite in equivalent exponential form as
\[(x-4)(x-14)=10^1=10\]assuming the log is base ten

Answer 3

so your final job is to solve the quadratic equation
\[(x-4)(x-14)=10\]
\[x^2-18x+56=10\]
\[x^2-18x+46=0\]etc

Answer 4

you need to check your answers, because you cannot take the log of negative number

Answer 5

got it thanks :)))

Answer 6

yw