Logarithmic and exponential functions

Write down the value of $\lg(10000)$.

Solve the equation $\log_2(\log_3 x) = 2$.

Solve the equation $\log_x 5 = \log_5 x^4$.

Write $\frac{1}{\log_x \mathrm{e}} - \ln(x - 1)$ as a single logarithm to base $\mathrm{e}$.

Solve the equation $2\log_5 2x = 1 + \log_5(9x - 10)$.

Write down the set of values of $x$ for which $\log_5(12x - 4)$ exists.

Solve the equation

Find $y$ in terms of $x$.

Find the value of $x$ when $y = \mathrm{e}^{25}$.

Write $5\lg a - 4\lg b - 3$ as a single base 10 logarithm.

Solve the equation $\log_5(x+1) - \log_{(x+1)} 5 = 0$.

$\log_5(5x - 2) - \log_{25} x = \frac{1}{2}$

$\mathrm{e}^{3y - 7} + \frac{4}{\mathrm{e}^3} = \frac{5}{\mathrm{e}^{3y - 1}}$