Raymond B. answered • 07/27/21
Math, microeconomics or criminal justice
log(7x+6) - log(x-7) = 1
log[(x+6)/(x-7)] = 1
(x+6)(x-7) = 10^1= 10 if you want to solve for x, expand the left side, combine constants and use the quadratic formula. x=-b/a + or - (1/a)sqr(b^2-4ac) when y=ax^2 +bx + c
basic formulas for logs for this problem are
loga - logb = log(a/b)
log10a = b can be rewritten as 10^b = a
log a or log anything usually means a common log to the base 10. In more advanced mathematics it's to base e, same as ln
IF that was implicit, base e, then
(x+7(x-6) = e = about 2.732
its solution is sort of messy.
Odds are the common log to base 10 was intended, although its solution is also messy
x^2 +x -42 = 10 or
x^2 +x -52 = 0
x=about 6.73 or -7.73 using the quadratic formula, but you could argue for a different solution and problem if log means natural log to the base e
