Solve the given equation:

${19}^x=2$

Solve the given equation:

${\mathrm{e}}^x=5$

Solve the given equation:

${\mathrm{e}}^x=10$

Solve the given equation:

$2^{4x}=9$

Solve the given equation:

$6^{3x}=4$

Solve the given equation:

$5^{\frac{1}{2}x}=79$

Solve the given equation:

$2^{x+1}=15$

Solve the given equation:

$6^{x-2}=4$

Solve the given equation:

${\mathrm{e}}^{x-1}-4=6$