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How do you solve \[\log x = 3\]

seo-qna
Last updated date: 17th Jun 2024
Total views: 373.8k
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Answer
VerifiedVerified
373.8k+ views
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.

Additional information:
Some properties of logarithm:
1) $\log (m.n) = \log m + \log n$
2) $\log \left( {\dfrac{m}{n}} \right) = \log m - \log n$
3) ${\log _b}({m^n}) = p{\log _b}(m)$
These are some important properties of logarithm through which the calculations are easy.

Note:
When we solve these questions the most important thing is the base so when we are solving the questions first thing we have to check the base because the value at the different base is different for the same question.