List of top Mathematics Questions on Exponential and Logarithmic Functions

Let $f(x) = \log_e(9x)$ for $x > 0$ and $h(x) = f(x) + f(x^2) + f(x^3)$. Then the value of $h(\frac{1}{3}e^{1/3})$ is equal to

If $y=e^{2x}+sin~x$, then $2y^{\prime\prime}-5y^{\prime}+2y=$}

The number of real roots of the equation \[ e^{3x}-2e^{2x}-e^{x}+2=0 \] is

If \[ \log_2(x-1)+\log_2(x-3)=3, \] then the value of \(x\) is

If \[ \log_a 2+\log_a 5=1, \] then the value of \(a\) is:

If \[ \log_2(x-1)+\log_2(x+1)=3, \] then \(x\) is equal to:

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

Solve for \(x\): \[ x+\log_{15}(5+3^x)=x\log_{15}5+\log_{15}24 \]

The range of the function $f(x)=\left(\frac{1}{3}\right)^{3+\sin x}$ is

If \(\log_8 x = \frac{1}{3}\), find the value of \(x\).

If $\log_a b = 2$, then $b = ?$

Find the function \( f \) which satisfies the equation \( \frac{df}{dx} = 2f \), given that \( f(0) = e^3 \)

If $f : \mathbb{R}^+ \to \mathbb{R}$ is defined as $f(x) = \log_a x$ where $a>0$ and $a \neq 1$, prove that $f$ is a bijection. (R$^+$ is the set of all positive real numbers.)

The sum of all the solutions of the equation \[(8)^{2x} - 16 \cdot (8)^x + 48 = 0\]is:

If \[ 4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}, \] then \[ x= \]

The sum of all the real roots of the equation \((e^{2x} – 4)(6e^{2x} – 5e^x + 1) = 0\) is

If \(x > 0\), then
\[ 1 + \frac{\log x}{1!} + \frac{(\log x)^2}{2!} + \cdots = \]

The solution of \( 3^{2x-1} = 81^{1-x} \) is:

The range of the function \(f(x) = \log_5(25 - x^2)\) is

If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax + b^2 = 0 \), then \( \alpha^2 + \beta^2 \) is equal to: