Hi, there-- The Problem-- Solve the equation log[a] 16 = -4 A Solution-- Often it's helpful with logarithm problems to translate them to exponent language. We have log base a of 16 is -4. In exponent language we have the number a raised to the -4 power to give 16. a^(-4) = 16 Rewrite this without the negative exponent. 1/(a^4) = 16 Solve for a. a^4 = 1/16 a = 4th root of 1/16. In other words, what number can I multiply by itself 4 times to give 1/16? (1/2)^4 = (1/2)*(1/2)*(1/2)*(1/2) = 1/16 a = 1/2 Let's check our answer. First in exponent language, then in logarithm language. Substitute 1/2 for a. a^(-4) = 16 (1/2)^(-4) = 16 1/((1/2)^4) = 16 1/(1/16) = 16 16 = 16 Check! log[a] 16 = -4 log[1/2] 16 = -4 -4 = -4 Check! Hope this helps! Contact me if you still have questions; I'll be happy to answer. Mrs.Figgy math.in.the.vortex@gmail.com