Math woes, some help?

Question

Alright, so I have this massive assignment, and I've done most of it, but I need some major aid on these problems. I don't even know where to start, so if someone can show me how to do these, I'd appreciate it. Please show me your work, just leaving the answers won't teach me anything :)

I will use the letter "v" to symbolize a down arrow, as I don't know how else to type logs.

Write as a single logarithm, 3 log (x) - 4 log (y) -5 log (z)

Expand, using log properties, to get 3 terms, logvb(15m^2p)

Solve using the properties of logarithms

logvx^7=4

2logv5^(x) = 2 + logv5^(4)

Answer 1

We recall the main properties of logarithms :
1) logva(xy) = logva x + logva y
2) logva(x/y) = logva x - logva y
3) logva (x^n) = n * logva (x)
4) logva (a) = 1
5) logva (1) = 0
Using this properties :
log (x) - 4 log (y) -5 log (z) = log (x) - log (y^4) - log (z^5)
= log ( x / ( y^4 * z^5))
* logvb(15m^2p) = logvb (3 * 5 * m^2p )
= logvb 3 + logvb 5 + logvb (m^2p)
= logvb 3 + logvb 5 + 2p * logvb (m)
Logva x^7 = 4 you didn't mention the base og the logarithm, i make it a
so 7 logva x = 4
so logva x = 4/7
so x = a^(4/7)
may you mean :
2 logv5 (x) = 2 + logv5 (4)
logv5 x^2 = logv5 (25) + logv5 (4) = logv5 ( 25*4) = logv5 (100)
so x^2 = 100
so x = 10 ( no logarithm for negative numbers )

Answer 2

Log Properties
1. LogA + LogB = Log(A*B)
2. LogA - LogB = Log(A/B)
3. LobA^x = XLog(A)
4. LogVaA = 1 and logva1 = 0
5. LogvaX = LogX/Loga = LinX/Lina

for 1 - 3 the logva are all the same va one can't be va and the other vb


-------------------------------------
3 log (x) - 4 log (y) -5 log (z)

Use the property 3 and 2

logx^3 - logy^4 - logz^5

log(x^3/y^4/z^5)

Reduce that (x^3/1) / (y^4/z^5) turn the fraction over to multiply.

(x^3)*(z^5/y^4)

Finally: Log(x^3z^5/y^4)

Answer 3

3log (x) - 4 log (y) -5 log (z)
=log(x^3) - log(y^4) - log(z^5)
= log(x^3)-log(y^4*z^5)
=log(x^3/(y^4*z^5))

logvb(15m^2p) = logvb(15) + logvb(m^2) + logvb(p)

logvx^7 doesn't make sense

2logv5^(x) = 2 + logv5^(4)

logv5^(x) doesn't make sense

Answer 4

log (x^3/y^4z^5)


log x^7 = 4, then 7logx =4, then logx = 4/7 then x = log^-1(4/7) x=3.7276