## Task $8 / 76$

Let $\log _{90} 3=a, \log _{90} 5=b$. Calculate $\log _{90} 8=f(a ; b)$.
It holds that $\log _{90} 8=3 \cdot \log _{90} 2$ (1) and

$$
\begin{gathered}
\log _{90} 90=\log _{90}\left(2 \cdot 3^{2} \cdot 5\right)=\log _{90} 2+2 \cdot \log _{90} 3+\log _{90} 5=1 \quad \text { so } \\
\log _{90} 2=1-2 \cdot \log _{90} 3-\log _{90} 5=1-2 a-b \quad \text { (2) }
\end{gathered}
$$

From (1) and (2) it immediately follows that $\log _{90} 8=3(1-2 a-b)$