# 5(10^x−6)=7

$$\displaystyle{5}{\left({10}^{{x}}−{6}\right)}={7}$$

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hajavaF
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: $$\displaystyle{x}={6}+{\log{{1.4}}}\sim{6.146}$$