5(10^x−6)=7

Kye 2021-08-15 Answered
\(\displaystyle{5}{\left({10}^{{x}}−{6}\right)}={7}\)

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Expert Answer

hajavaF
Answered 2021-08-16 Author has 14809 answers
We are given: \(\displaystyle{5}{\left({10}^{{x}}−{6}\right)}={7}\)
Divide both sides by 5: \(\displaystyle{10}^{{x}}-{6}={1.4}\)
Take the (common) logarithm of both sides: \(\displaystyle{{\log{{10}}}^{{x}}-}{6}={\log{{1.4}}}\)
Recall that \(\displaystyle{\log{{b}}}\cdot{b}^{{x}}={x}\) and since the common logarithm is base 10, we write: \(\displaystyle{x}-{6}={\log{{1.4}}}\)
Add 6 to both sides: \(\displaystyle{x}={6}+{\log{{1.4}}}\sim{6.146}\)
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