Question

Lg7/5-lg8/5 + lg8/7-lg1/100

Answer 1

Ответ:

2

Объяснение:

lg(7/5)-lg(8/5)+lg(8/7)-lg(1/100)=lg(7×5×8/(5×8×7))-lg10⁻²=lg1+2lg10=0+2=2

Answer 2

To simplify the expression:

lg(7/5) - lg(8/5) + lg(8/7) - lg(1/100)

You can use the properties of logarithms to combine and simplify these terms:

lg(7/5) + lg(8/7) - (lg(8/5) + lg(1/100))

Now, let's use the properties of logarithms:

lg(7/5 * 8/7) - lg(8/5 * 1/100)

Now, calculate the products inside the logarithms:

lg(56/35) - lg(8/500)

Next, simplify the fractions:

lg(8/5) - lg(4/250)

Now, we can simplify further:

lg(8/5) - lg(1/62.5)

Use the property of logarithms where lg(a) - lg(b) is equal to lg(a/b):

lg((8/5) / (1/62.5))

Now, calculate the division:

lg((8/5) * 62.5)

lg(500)

So, the simplified expression is lg(500).