Answer:
x = 3^(1/13) ≈ 1.08818224346
Explanation:
You want to solve for x the equation ...
log(10) +13·log(x) = log(30) . . . . where logs are to the base 'a'
Solution
Solving the equation for log(x), we have ...
13·log(x) = log(30) -log(10)
log(x) = (1/13)·log(30/10)
Taking antilogs (base 'a'), we have ...
x = 3^(1/13)
The numerical value of this is about 1.08818224346.
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Additional comment
We made use of the relations ...
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
These relations hold for logs to any base.
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