Recent questions tagged logarithms

The value of $\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$ is$0$ $1$ $-1$ None of these

Consider two distinct positive real numbers $m, n$, with $m>n$. Let $x=n^{\log _{10}(m)}$ and $y=m^{\log _{10}(n)}$. The relation between $x$ and $y$ is $\_\_\_\_$.$x>y$$...

Let $x,$ $y,$ $z$ be positive numbers such that $x^{2}+y^{2}=z^{2}$. Determine the value of the following expression:$$\frac{\log _{y+z} x+\log _{z-y} x}{\left(\log _{y+z...

Let $N=2^{150}$. How many bits are required to write $N$ in binary (base $2$)? How many digits are required to write $N$ in decimal (base 10)? You may assume that $\log _...

If \( y = \sqrt[3]{5 \sqrt[3]{5 \sqrt[3]{5 \cdots}}} \), then the value of \( \log_{25} y \) is _____.A. \(\frac{1}{5}\)B. \(\frac{1}{4}\)C. \(\frac{1}{3}\)D. \(\frac{1}{...

For positive non-zero real variables $x$ and $y$, if\[\ln \left(\frac{x+y}{2}\right)=\frac{1}{2}[\ln (x)+\ln (y)]\]then, the value of $\frac{x}{y}+\frac{y}{x}$ is$1$$1 / ...

For positive non-zero real variables $p$ and $q$, if$\log \left(p^2+q^2\right)=\log p+\log q+2 \log 3,$then, the value of $\frac{p^4+q^4}{p^2 q^2}$ is$79$$81$$9$$83$

What will be the value of the following expression?$$\frac{1}{\log _a a b c}+\frac{1}{\log _b a b c}+\frac{1}{\log _c a b c}$$

What will be value of $x$ satisfying the below equation?$$\sqrt{\log _2 x^4}+4 \log _4 \sqrt{\frac{2}{x}}=2$$

Which of the following is true ?$ \log_{17} 275 = \log_{19} 375$$ \log_{17} 275 \log_{19} 375$$ \log_{17} 275 < \log_{19} 375$None of the these

$\log (x+3) + \log (x+5) = \log 35,$ solve for $x$ :$1$$2$$3$$4$

$ \dfrac{1}{2}\; \log_{10}25 – 2 \log_{10}3 + \log_{10}18$ equals $:$$18$$1$$\log_{10}3$None of these

Which of the following is true ? $\log_{17} 275 = \log_{19} 375$$\log_{17} 275 \log_{19} 375$$\log_{17} 275 < \log_{19} 375$None of these

Let $x_1 x_2>0$. Then which of the following is true?$\log \big(\frac{x_1+x_2}{2}\big) \frac{\log x_1+ \log x_2}{2}$$\log \big(\frac{x_1+x_2}{2}\big) < \frac{\log x_1+ ...