Question

Log5(30)/log30(5)-log5(150)/log6(5)

Answer 1

Смотри во вложении.

Answer 2

Log(5)30=log(5)(5*6)=log(5)5+log(5)6=1+log(5)6
log(30)5=1/log(5)30=1/(1+log(5)6)
log(5)150=log(5)(25*6)=log(5)25+log(5)6=2+log(5)6
log(6)5=1/log(5)6
получим
(1+log(5)6):1/(1+log(5)6)-(2+log(5)6):1/log(5)6=
=(1+log(5)6)²-(2+log(5)6)*log(5)6=
=1+2log(5)6+log²(5)6-2log(5)6-log²(5)6=1

Answer 3

To simplify the given expression, let's break it down step by step:

1. Logarithmic identities:
   • logₐ(b) / logₐ(c) = log_c(b)

Using this identity, we can rewrite the expression:

Log₅(30) / Log₃₀(5) - Log₅(150) / Log₆(5) = Log₃₀(30) - Log₆(150)

2. Logarithmic conversions:
   • Logₐ(b) = Logₓ(b) / Logₓ(a)

Applying this conversion to both terms:

Log₃₀(30) = Log₆(30) / Log₆(30) Log₆(150) = Log₆(150) / Log₆(6)

So the expression becomes:

Log₆(30) / Log₆(30) - Log₆(150) / Log₆(6)

3. Simplification: Since Logₓ(x) = 1 for any base x, we can simplify the expression further:

1 - Log₆(150) / Log₆(6)

4. Calculations: Calculate the logarithms:

Log₆(150) ≈ 2.598 Log₆(6) = 1

Substitute these values into the expression:

1 - 2.598 / 1 ≈ -1.598

So, the simplified value of the expression is approximately -1.598.