Logarithmic Equation

[lukash]

i'm new in this forum and made some mistakes.
this is the exercise:
[tex]log_{1/2}(x - 1) - log_2(x + 1) - log_{1/\sqrt{2}}(7 - x) = 1[/tex]

[Math Tutor]

Use the formulas here:
http://www.math10.com/en/algebra/logari ... ln-lg.html

1) use the formula: [tex]log_bc = log_ac / log_ab[/tex]

and make all logarithms bases 2

log_1/2(x-1) = log₂(x-1) / log₂(1/2)

[tex]1/2 = 2^{-1}[/tex] so [tex]log_2(1/2) = log_2(2^{-1}) = -1[/tex]

then we have:

[tex]-log_2(x-1) - log_2(x+1) + 2log_2(7 - x) = 1[/tex]

and we will use the formula: log_a(b.c) = log_ab + log_ac

so: [tex]-( log_2(x-1)(x+1) ) = -(2log_2(7 - x)-1)[/tex]

[tex]1 = log_22[/tex]

and [tex]2log_2(7 - x) = log_2(7 - x)^2[/tex]

so: [tex]log_2(x-1)(x+1) = log_2((7 - x)^2/2)[/tex]

I think you do not need more help about this logarithmic equation

[Kenyon Ansel]

Hey, I'm having problems combining these 2 logarithm problems. Could someone kindly solve it with steps shown for me? I'd really be grateful!

Use the Laws of Logarithms to combine the expression.
-5log3 A - 3log3 B + 5log3 C = log3

Use the Laws of Logarithms to combine the expression.
-2ln 5 + 4ln x + 3ln (x2 + 5) = ln

Thanks so much!

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