Consider the following statements in respect of common logarithms : I. The logarithm of a number greater than 100 but less than 1000 lies between 2 and 3. II. The logarithm of a positive number less than unity is negative. Which of the statements given above is/are correct?
Both I and II
Since \(\log_{10}100 = 2\) and \(\log_{10}1000 = 3\), and the logarithm function is increasing, for \(100 < N < 1000\) we get \(2 < \log_{10}N < 3\), so statement I is correct. For any positive \(0 < x < 1\), \(\log_{10}x < 0\), so statement II is also correct. Hence both I and II are correct.
Similar Questions
If \(a^b = b^a\), then what is
\(\frac{a \times (\frac{a}{b}) ^{ \frac{a}{b} } }{ (a)^{ \frac{a}{b} } }\)
equal to?
- If \(\alpha\) and \(\beta\) are the roots of the equation \(\log_{10} [998+\sqrt{x^2-18x+76}] = 3\) then what is \((\alpha - \beta)^2\) equal to?
If \(x^4 + y^4 = 14x^2 y^2\), then consider the following :
I. \(\log_{10}(x^2 + y^2)\) = \(\log_{10} x + \log_{10} y + 2\log_{10} 2\)
II. \(\log_{10}(x^2-y^2)=\log_{10} x + \log_{10} y\) +\(\log_{10}2+0.5\log_{10} 3\)
Which of the above is/are correct?
- If \(\log_{10}2 = 0.301\) and \(\log_{10} 3 = 0.477\), then what is the number of digits in the expansion of \(60^{60}\) ?
If log10(100001 - 4x)/(5 - x) = 1, then what is x equal to?
What is √17 - 4√15 + √8 - 2√15 equal to?
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What is the number of zeros immediately after the decimal point in \((0.5)^{1000}\)? (Given that \(\log_{10}2 = 0.30103\))
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Important Questions from Logarithms
Given that $132^{0.14} = x$, $132^{0.26} = y$ and $x^z = y^2$, then the value of z is close to:
For \(x \ge y > 1\), let \(\log_x\left(\frac{x}{y}\right) + \log_y\left(\frac{y}{x}\right) = k\), then the value of \(k\) can never be equal to
If \(\log_ba = p\), \(\log_dc = 2p\) and \(\log_fe = 3p\), then what is \((ace)^{\frac{1}{p}}\) equal to ?
- What is the number of solutions of \(\log_4(x-1) = \log_2(x - 3)\)?
- Let \(p = \ln(x)\), \(q = \ln(x^3)\) and \(r = \ln(x^5)\), where \(x > 1\). Which of the following statements is/are correct?
I. \(p, q\) and \(r\) are in AP.
II. \(p, q\) and \(r\) can never be in GP.
Select the answer using the code given below.
