Laws of Indices and Logarithms

Simplify the following expression: 2^a × 2^(a+2) ÷ 2^(2a −3)

Simplify 3^(n+1) ÷ 27^(5n +2) × 9^n

Simplify 2^(x^5) y^2 × 8^(x^2) y^6

Solve the following 2y^(3/2) = 54

Solve the following 6^(1−y) = 36

Solve the following 3^(2x) − 10(3^x) = −9

Express 2^5 = 32 in logarithmic form.

Express 2^5 = 32 in logarithmic form.

Convert log_2 8 = 6 to index form.

Express log_a e^2 q^3 by using Laws of logarithms.