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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
