Finding unknown in log equation I was given a log equation: D=10log(I/I_0) I is the unknown in this case, I_0=10^(−12) and D=89.3.

targetepd 2022-08-12 Answered
Finding unknown in log equation
I was given a log equation:
D = 10 log ( I / I 0 )
I is the unknown in this case, I 0 = 10 12 and D = 89.3
I did the following steps:
  89.3 = 10 log ( I 10 12 )   89.3 10 = log ( I 10 12 )   8.93 = log ( I 10 12 )
I'm not quite sure how to isolate I after step 3, and I'm also unsure if dividing 89.3 / 10 is correct as well. So how can I find the unknown ( I)?
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Answers (2)

Luna Wells
Answered 2022-08-13 Author has 19 answers
Yes you are on the right track. For logarithms we have
log a y = x a x = y
Here's a tip: log ( I 10 12 ) = log ( 10 12 I ) . So then we have
8.93 = log 10 ( 10 12 I ) 10 8.93 = 10 12 I 10 8.93 12 = I I = 10 3.07
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sarahkobearab4
Answered 2022-08-14 Author has 5 answers
You're on the right way. You need to find the function f so that f ( l o g ( x ) ) = x
Hint
x R , l o g a ( a x ) = x , a R
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