List of top Mathematics Questions on Logarithms

If the domain of \[ f(x)=\log_{(10x^2-17x+7)}\,(18x^2-11x+1) \] is $(-\infty,a)\cup(b,c)\cup(d,\infty)-\{e\}$, then find $90(a+b+c+d+e)$.

The sum of all the real solutions of the equation \[ \log_{(x+3)}\left(6x^2 + 28x + 30\right) = 5 - 2\log_{(6x+10)}\left(x^2 + 6x + 9\right) \] is equal to .

Sum of solutions of the equation \[ \log_{x-3}(6x^2 + 28x + 30) = 5 - 2\log_{x-10}(x^2 + 6x + 9) \] are:

If \( a, b, c \) are positive real numbers each distinct from unity, then the value of the determinant \[ \left| \begin{matrix} 1 & \log_a b & \log_a c \\ \log_b a & 1 & \log_b c \\ \log_c a & \log_c b & 1 \end{matrix} \right| \] is:

\(\text{Let } S = \{x \in \mathbb{R} : (\sqrt{3} + \sqrt{2})^x + (\sqrt{3} - \sqrt{2})^x = 10\}\).Then the number of elements in \( S \) is:

Consider the function f(x) = (x−2)logx. Then the equation xlogx = 2−x has:

The value of \( x (\log y - \log z) \times y (\log z - \log x) \) is equal to:

The value of \( \log \frac{14}{15} - \log \frac{3}{25} - \log \frac{7}{9} \) is:

The value of \( \log_5 \left( \frac{1}{125} \right) \) is:

If for $x, y \in \mathbb{R}, x>0, y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \dots$ upto $\infty$ terms and $\frac{2 + 4 + 6 + \dots + 2y}{3 + 6 + 9 + \dots + 3y} = \frac{4}{\log_{10} x}$, then the ordered pair $(x, y)$ is equal to :

If $\log_3 2, \log_3(2^x-5), \log_3(2^x-\frac{7}{2})$ are in an arithmetic progression, then the value of x is equal to _________.