a) The equation can be solved as follows:
[tex]\begin{gathered} \log _78+\log _79=\log _78\times9=\log _78+\log _79=\log _772 \\ \log _78+\log _79=\log _772 \end{gathered}[/tex]
So the value in the box is 72.
b)Let the unknown value be x:
The equation can be solved as follows:
[tex]\begin{gathered} \log _8x-\log _83=\log _8\frac{5}{3} \\ \log _8x=\log _8\frac{5}{3}+\log _83 \\ \log _8x=\log _8\frac{5}{3}\times3 \\ \log _8x=\log _85 \end{gathered}[/tex]
So the value in the box is 5.
c)Let the unknown value be x:
The equation can be solved as follows:
[tex]\begin{gathered} \log _681=4\log _6x \\ \log _681=\log _6x^4 \\ 81=x^4 \\ x^4=3^4 \\ x=3 \end{gathered}[/tex]
So the value in the box is 3.
