Question

URGENT HELP ME PLEASE

1) Develop the LOGARITHM PROPERTIES AND SOLVE THE EQUATIONS:


a-) log3 (81.3) =

b-) log5 (625.25) =

c-) log2 64/8 =

d-) log464/16 =

e-) log6 (364) =

f-) log (1003) =

Answer 1

(a)
`\log_3((81)/(3))=3`

(b)
`\log_5((625)/(25))=2`

(c)
`\log_2((64)/(8))=3`

(d)
`\log_4((64)/(16))=1`

(e)
`\log_6(36^4)=8`

(f)
`\log(100^3)=6`

Explanation:

Let as consider the given equations are
`\log_3((81)/(3))=?,\log_5((625)/(25))=?,\log_2((64)/(8))=?,\log_4((64)/(16))=?,\log_6(36^4)=?,\log(100^3)=?`.

(a)

`\log_3((81)/(3))=\log_3(27)`

`\log_3((81)/(3))=\log_3(3^3)`

`\log_3((81)/(3))=3`
`[\because \log_aa^x=x]`

(b)

`\log_5((625)/(25))=\log_5(25)`

`\log_5((625)/(25))=\log_5(5^2)`

`\log_5((625)/(25))=2`
`[\because \log_aa^x=x]`

(c)

`\log_2((64)/(8))=\log_2(8)`

`\log_2((64)/(8))=\log_2(2^3)`

`\log_2((64)/(8))=3`
`[\because \log_aa^x=x]`

(d)

`\log_4((64)/(16))=\log_4(4)`

`\log_4((64)/(16))=1`
`[\because \log_aa^x=x]`

(e)

`\log_6(36^4)=\log_6((6^2)^4)`

`\log_6(36^4)=\log_6(6^8)`

`\log_6(36^4)=8`
`[\because \log_aa^x=x]`

(f)

`\log(100^3)=\log((10^2)^3)`

`\log(100^3)=\log(10^6)`

`\log(100^3)=6`
`[\because \log10^x=x]`