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# How do you solve $\log x = 3$

Last updated date: 17th Jun 2024
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Hint: In order to solve this question we should know the base of the logarithm but as it is not given in question so we will assume the base to be 10. And according to this base, we will solve this question. After this, we will apply the properties of the log and get the final solution.

Complete step by step solution:
For solving these types of problems we need to know the base in question. The base is not mentioned so in general, we assume it as 10.
So the question will be:
${\log _{10}}x = 3$ ………………… (1)
Now by applying the property of logarithm:
If,
${a^{{{\log }_a}b}} = {a^c}$
Then,
b=c
Now taking 10 to the power of (1) we get:
${10^{{{\log }_{10}}^x}} = {10^3}$

According to the property, we will get the value of x = 3.

1) $\log (m.n) = \log m + \log n$
2) $\log \left( {\dfrac{m}{n}} \right) = \log m - \log n$
3) ${\log _b}({m^n}) = p{\log _b}(m)$