Asked by Natalie
What is the real value of x in the equation log(subscript 2)24-log(subscript 2)3=log(subscript 5)x?
I really cannot remember at all how logs work. I know the answer is 125 but have no idea how to get there. Thanks in advance.
I really cannot remember at all how logs work. I know the answer is 125 but have no idea how to get there. Thanks in advance.
Answers
Answered by
Reiny
Two things to remember
1. log<sub>a</sub> x = y is the same as a<sup>y</sup> = x
2. Log A - Log B = Log (A/B) as long as the bases are the same
so log(subscript 2)24-log(subscript 2)3=log(subscript 5)x
log<sub>2</sub>(24/3) = log<sub>5</sub> x
log<sub>2</sub>8 = log<sub>5</sub> x
3 = log<sub>5</sub> x
5^3 = x
125 = x
1. log<sub>a</sub> x = y is the same as a<sup>y</sup> = x
2. Log A - Log B = Log (A/B) as long as the bases are the same
so log(subscript 2)24-log(subscript 2)3=log(subscript 5)x
log<sub>2</sub>(24/3) = log<sub>5</sub> x
log<sub>2</sub>8 = log<sub>5</sub> x
3 = log<sub>5</sub> x
5^3 = x
125 = x
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