Question

How do you solve \[\log 4x=2\]?

Answer 1

Hint: From the given question, we have been asked to solve \[\log 4x=2\]. We can solve the given question by using some basic formulae of logarithms. First of all, we have to rewrite the given logarithmic equation into the simplified form and then we have to use some basic formulae of logarithms to solve it.

Complete answer:
From the question, we have been given that \[\log 4x=2\]
We know that logarithms with a base of \[10\] . \[\left( {{\log }_{10}}x \right)\] are commonly rewritten without it \[\left( \log x \right)\].
After writing the given question with a base, then the given equation will become \[{{\log }_{10}}4x=2\]
Now, as we have already discussed above, after rewriting the given equation, we have to apply one of the basic formulas of logarithms to solve the given equation in the given question.
Now, as of process we have to apply one of the basic formulae of logarithms.
In logarithms, we have one basic formula, that is
If \[{{\log }_{a}}b=x\], then it can be \[{{a}^{x}}=b\].
Now, let us apply the above condition to our equation.
By applying the above condition for our equation, we get
\[{{\log }_{10}}4x=2\]
\[\Rightarrow {{10}^{2}}=4x\]
On furthermore simplifying the equation, we get \[100=4x\]
Shift \[4\] from the right hand side of the equation to the left hand side of the equation. Then we get \[\dfrac{100}{4}=x\]
Therefore, $x=25$
Hence, the given logarithmic equation is solved.

Note: We should be very careful while applying the conditions of logarithms. Also, we should be very careful while doing the calculation. Also, we should be well aware of the basic formulae of logarithms and also they should know how to use the formula. Also, we should be very careful while using the conditions of logarithms because they are quite confusing conditions. We have many logarithms formulae like $\log ab=\log a+\log b$ , $\log \left( \dfrac{a}{b} \right)=\log a-\log b$ and many more.