Express as a single logarithm and simplify if possible 14 lo

Express as a single logarithm and simplify, if possible. 1/4 log_b x + 2 log_b y - 4 log_b x 1/4 log_b x + 2 log_b y -4 log_b x = (Type your answer using exponential notation. Use integer

Solution

We have given (1/4)log_bx+2log_by-4log_bx

(1/4)log_bx+2log_by-4log_bx=2log_by-(15/4)log_bx since adding (1/4)log_bx-4log_bx=-15/4log_bx

=log_by^2-log_bx^(15/4)

=log_b(y²/x^(15/4))

(1/4)log_bx+2log_by-4log_bx =log_b(y²/x^(15/4))