Question

Log5 22-log5 11- log5 10 2log7 32 -log7 256 -2log7 14 log4 5+log4 25+ log4 125/2

Answer 1

Ответ:

Объяснение:

$1)\;log_522-log_511-log_510=log_5\frac{22}{11*10}=log_5\frac{1}{5}=log_55^{-1}=-1\\\\2)\;2log_732-log_7256-2log_714 = log_732^2-log_7256-log_714^2=log_7\frac{1024}{256*196}=log_7\frac{1}{49}=log_77^{-2}=-2\\\\3)\;log_45+log_425+log_4\frac{125}{2}=log_4\frac{5*25*125}{2}=log_{2^2}\frac{5*5^2*5^3}{2}=\frac{1}{2}log_2\frac{5^6}{2}=log_2\frac{5^3}{\sqrt{2} }=log_25^3-log_22^{\frac{1}{2} }=log_25^3-\frac{1}{2}$

Answer 2

Let's simplify each expression step by step:

1. Logarithmic properties:
   • log_a(b) - log_a(c) = log_a(b/c)
   • log_a(b^n) = n * log_a(b)

Using these properties:

• log5(22) - log5(11) - log5(10) = log5(22/11) - log5(10) = log5(2) - log5(10)

2. log7(32) - log7(256) - 2 * log7(14) = log7(32/256) - log7(14^2) = log7(1/14^2) = log7(1/196)

3. log4(5) + log4(25) + log4(125/2) = log4(5 * 25 * (125/2)) = log4(3125/2)

Now, you have three simplified expressions:

1. log5(2) - log5(10)
2. log7(1/196)
3. log4(3125/2)

You can further simplify these expressions if needed or calculate their decimal values if you have specific numerical values for the logarithmic bases.