Write the expression below as a single logarithm in simplest form.

2 log_b 4 + log_b 2

We want to write the expression,

2log_b4+log_b2 as a single logarithm.

We have,

2log_b4+log_b2

=log_b4²+log_b2

(since nlog_bm=log_bmⁿ )

=log_b16+log_b2

=log_b(16.2)

(since log_bm+log_bn=log_b(m.n) )

=log_b(32)

Thus,

2log_b4+log_b2=log_b(32), using some logarithmic rules.

Hence the expression,

2log_b4+log_b2 as a single logarithm log_b(32)