Question

1) log12 3 + log12 4 2) log7 98 - log7 2 3) log2 5 - log2 35 + log2 56 4) log1/3 5 - log1/3 5 + log1/3 9 как сможете 1) lg4 + lg250 2) log2 6 - log2 6/32 3) (log12 4 + log12 36)^2 4) lg13 - lg130 5) (log2 13 - log2 52)^5 6) (log0,3 9 - 2log0,3 10)^4 решите уравнение 1) log3 x = -1 2) log2 x = -5 3) log3 x = 2 4) log4 x = 3 5) log4 x = -3 6) log7 x = 0 7) log1/7 x = 1 8) log1/2 x = -3 вычислите 1) log2 log2 log3 81 2) log2 log3 log1/3 1/27 3) log√3 log5 125 4) log4 log3 81 как сможете заранее

Answer 1

1) log₁₂3 + log₁₂4 = log₁₂(3*4) = log₁₂12 = 1
2) log₇98 - log₇2 = log₇(98/2) = log₇49 = 2
3) log₂5-log₂35 + log₂56 = log₂(5/35) + log₂56 = log₂($\frac{5*56}{35})=$log₂8 = 3
4) log₁/₃5 - log₁/₃5 + log₁/₃ 9 = log₁/₃9 = -2

1) lg4 + lg250= lg(4*250) = lg1000 = 3
2) log₂6 - log₂$\frac{6}{32}$ = log₂($\frac{6*32}{6})$ = log₂32 = 5
3) (log₁₂4 + log₁₂36)² = (log₁₂144)² = 2² = 4
4) lg13 - lg 130 = lg$\frac{13}{130}$ = lg$\frac{1}{10}$ = -1
5) (log₂13-log₂52)⁵ = (log₂$\frac{13}{52}$)⁵ = (log₂$\frac{1}{4}$)⁵ = (-2)⁵ = -32
6) (log₀.₃9 - 2log₀.₃10)⁴ = (log₀.₃9 - log₀.₃100)⁴ = (log₀.₃$\frac{9}{100}$)⁴ = (log₀.₃0.09)⁴ = 2⁴ = 16

1) log₃x = -1
x = 3⁻¹ = 1/3
2) log₂x = -5
x = 2⁻⁵ = 1/32
3) log₃x = 2
x = 3² = 9
4) log₄x = 3
x = 4³ = 64
5) log₄x = -3
x = 4⁻³ = 1/64
6) log₇x = 0
x = 7° = 1
7) log₁/₇x = 1
x = 1/7
8) log₁/₂x = -3
x = (1/2)⁻³ = 8

1) log₂log₂log₃81 = log₂log₂4 = log₂2 = 1
2) log₂log₃log₁/₃(1/27) = log₂log₃3 = log₂1 = 0
3) $log_{ \sqrt{3} }$log₅125 = $log_{ \sqrt{3} }$3 = 2
4) log₄log₃81 = log₄4 = 1