Question

solve the euation log x + log (x+3) =1


solve the equation algebraically 2e^x=6 -e^-x


find the functions f and g so that f*g = h ... h(x)=(6x+9)^8

write the expression as a single log express power as factors:ln (x/x-1) + ln(x+1/x) -ln (x^2-1)

Answer 1

aw of logs: log a + log b = log (ab)

log x + log (x-3) = 1
log x(x-3) = 1

x^2 - 3x = 10 (def. of log says log a = b when 10^b = a)

x^2 - 3x - 10 = 0

(x - 5)(x + 2) = 0

x = 5, x = - 2 (not possible b/c domain of log function is x>0)

Therefore, x = 5

Answer 2

thats the first one