Question 956322
log3(6) + log3(3x+1) = 21


log3(6) + log(3x+1) is the same as log3(6 * (3x+1)) which is the same as:


log3(18x + 6)


your equation becomes log3(18x+6) = 21


this is true if and only if 3^21 = 18x + 6


subtract 6 from both sides of this equation to get:


3^21 - 6 = 18x


divide both sides of this equation by 18 to get:


(3^21 - 6) / 18 = x


solve for x to get x = 581130733.2


that's your solution.


replace x with 581130733.2 in the original equation to get:


log3(6) + log3(3*581130733.2+1) = 21


simplify to get:


log3(6) + log3(1743392201) = 21


convert log base 3 to log base 10 using the conversion formula of log3(a) = log10(a)/log10(3) which can also be shown as log(a)/log(3).


your equation becomes:


log(6)/log(3) + log(1743392201)/log(3) = 21


use your calculator log function to evaluate this equation to get:


21 = 21


this conforms your solution is correct.