Logarithms

Solve for x: log⁡₂⁡(x−3)+log₂(x+5)=3

If log_⁡ab=2 and log⁡_bc=3, find log_⁡ac.

Simplify [Tex]\log \left(\frac{1000 \cdot \sqrt{10}}{10^3}\right)[/Tex]

If log_⁡x 2 = a and log⁡_x 5 = b, express log⁡_x 20 in terms of a and b.

Evaluate: log_⁡4 8 + log_⁡8 4

If log_⁡x 4 = 2 and log_⁡x 8 = 3, find x.

Solve for x if log⁡₃ (x+1) − log_⁡3 (x−1) = 1

If log_⁡5 (3x−7) = 2, find x

Solve the following logarithmic equation for x .

2log_ax = log_a18 + log_a(x-4).

If log_⁡3 x = 5, find log⁡₉ x