Calculation:

The 200000 represents the value of y. Plug in y as 200000 then solve it for x.

Solve the equation for x.

Divide both sides by 192.

\(\displaystyle{1041.6667}={\left({4}\right)}^{{{x}-{3}}}\)

Now, take log on both sides

\(\displaystyle{\log{{\left({1041.6667}\right)}}}={{\log{{\left({4}\right)}}}^{{{x}-{3}}}}\)

Divide both sides by log 4

\(\displaystyle{5.0123}={x}-{3}\)

Add both sides 3.

\(\displaystyle{8.0123}={x}\)

Conclusion:

Approximately after 8 hours, the bacteria culture became 200,000.

The 200000 represents the value of y. Plug in y as 200000 then solve it for x.

Solve the equation for x.

Divide both sides by 192.

\(\displaystyle{1041.6667}={\left({4}\right)}^{{{x}-{3}}}\)

Now, take log on both sides

\(\displaystyle{\log{{\left({1041.6667}\right)}}}={{\log{{\left({4}\right)}}}^{{{x}-{3}}}}\)

Divide both sides by log 4

\(\displaystyle{5.0123}={x}-{3}\)

Add both sides 3.

\(\displaystyle{8.0123}={x}\)

Conclusion:

Approximately after 8 hours, the bacteria culture became 200,000.