Question

The logarithmic expression a1" title="log_{b}(\frac{1}{b^{-b}} )" alt="log_{b}(\frac{1}{b^{-b}} )" align="absmiddle" class="latex-formula"> where b > 0, is equal to
a) $b^{-b}$

b) $b^{b}$

c) $-b$

d) $b$

Answer 1

$\log_b \left(\dfrac 1{b^{-b}}\right)\\\\=\log_b (b^{-b})^{-1}\\\\=\log_b b^b\\\\=b \log_b b\\\\=b \cdot 1\\\\=b$