Question

1)Log2×5-log2×35+log2×56
2)log5^2×x-log5×x-2=0
3) log1/3^3×1/9

Answer 1

1) $log_{2}$ 5 - $log_{2}$ 35 + $log_{2}$ 56 = $log_{2}$ $\frac{5}{35}$ + $log_{2}$ 56 = $log_{2}$ $\frac{1}{7}$ + $log_{2}$ 56 = $log_{2}$ ($\frac{1}{7}$ × 56) = $log_{2}$ 8 = 3

2) $log_{5^{2} }$ x - $log_{5}$ x - 2 = 0

2 × $log_{5}$ x - $log_{5}$ x = 2

$log_{5}$ x = $log_{5}$ 25

x = 25 = ± 5

3) $log_{(\frac{1}{3})^{3} }$ $\frac{1}{9}$ = $\frac{1}{3}$ × $log_{\frac{1}{3} }$ $\frac{1}{9}$ = $\frac{1}{3}$ × 2 = $\frac{2}{3}$