If log sub(a)10 = 0.250, then log sub(10)a equals ? Breakdown: log sub(a)10 = 0.250 The solution requires me to the take the base(a) anti logarithm of both sides. That would be 10 = a^(0.250).

lollaupligey9

lollaupligey9

Answered question

2022-08-02

If log sub(a)10 = 0.250, then log sub(10)a equals ?
Breakdown:
log sub(a)10 = 0.250
The solution requires me to the take the base(a) antilogarithmof both sides. That would be
10 = a 0.250 .

Answer & Explanation

neglegir86

neglegir86

Beginner2022-08-03Added 12 answers

log a ( 10 ) = 0.250
log 10 ( a ) = ?
note when no base is written, it is assumed base 10.
Using properties of logarithms, you get
log a ( 10 ) = log ( 10 ) / log ( a ) = 0.250
log 10 ( a ) = log ( a ) / log ( 10 ) = 1 / 0.250 = 4
zabuheljz

zabuheljz

Beginner2022-08-04Added 1 answers

log a ( 10 ) = 0.25
to
10 = a 0.25
This is because the antilog IS the power; the exponential function is the inverse of the logarithm:
a log a ( x ) = x and log a ( a x ) = x
That is, the functions
f ( x ) = a x
and
g ( x ) = log a ( x )
are inverses of one another; f(g(x)) = x and g(f(x)) = x for any x.
Therefore, we can undo the base-a logarithm by raising a to that power:
log a ( 10 ) = 0.25
a l o g a ( 10 ) = a 0.25 raising a to each power
10 = a 0.25 using the inverse (with x=10)
That's all there is to it.

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