SOLUTION: log [subscript 19] (10-2a) = log [subscript 19} (-3a-6) I got -5 is not equal to 2, no solution

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: log [subscript 19] (10-2a) = log [subscript 19} (-3a-6) I got -5 is not equal to 2, no solution       Log On


   

Question 1082046: log [subscript 19] (10-2a) = log [subscript 19} (-3a-6)
I got -5 is not equal to 2, no solution
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
log [subscript 19] (10-2a) = log [subscript 19} (-3a-6)
I got -5 is not equal to 2, no solution
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log%2819%2C%2810-2a%29%29 = log%2819%2C%28-3a-6%29%29  ====>

10-2a = -3a - 6.


Solve this VERY SIMPLE linear equation and obtain the answer a = -16.


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
log%2819%2C%2810-2a%29%29=log%2819%2C%28-3a-6%29%29

Same base; the inputs to the logs on both sides are equal.
10-2a=-3a-6
-2a%2B3a=-6-10
highlight%28a=-16%29

Are the logs of the original expressions those of positive number inputs, or non-negative inputs?

10-2%28-16%29=10%2B32=42
-
-3%28-16%29-6=48-6=42
-
Solution works.