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goblinko [34]
3 years ago
9

H=K+log(a/c) isolate a

Physics
2 answers:
Soloha48 [4]3 years ago
3 0
H=k+log(a/c)
H-k = log(a/c)
e^{h-k}=a/c
a = ce^{h-k}
dexar [7]3 years ago
3 0
Remember some properties
is no base is stated, assume base 10
and
log_a(b)=c means a^c=b
and
a^{log_a(b)}=b
and
log_a(b/c)=log_a(b)-log_a(c)
and
x^{a+b}=(x^a)(x^b)
so

H=K+log(a/c)
H=K+log_{10}(a/c)
H=K+log_{10}(a)-log_{10}(c)
minus K-log10(c) from both sides
H-K+log_{10}(c)=log_{10}(a)
convert
10^{H-K+log_{10}(c)}=a
(10^{H-K}(10^{log_{10}(c)}=a
(10^{H-K})(c)=a
a=c10^{H-K}
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