Properties of Logarithms

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It has been about a year since I have done some calculus and I am stuck on a few logarithm problems:

I have to combine the expression here:
(the coefficients are what are throwing me a curve. I know a multiplication problem expands to addition and vice versa, but I am a little lost)

-3 ln (x) + 1/2 ln [(x^2) + 5]

Also, on these next two I have to solve for x. I know it deals with some properties of logs, but I am afraid that I do not remember the properties

3^(x-2) = 5^2x

log base 3 of (2x+7) = 2

Sorry that I cannot show you any work, but frankly I am lost.

 

[Deleted member 4993]

It has been about a year since I have done some calculus and I am stuck on a few logarithm problems:

I have to combine the expression here:
(the coefficients are what are throwing me a curve. I know a multiplication problem expands to addition and vice versa, but I am a little lost)

-3 ln (x) + 1/2 ln [(x^2) + 5]

Also, on these next two I have to solve for x. I know it deals with some properties of logs, but I am afraid that I do not remember the properties

Why not dust off those ole text books and give it a go - refresh your memory!!

3^(x-2) = 5^2x

log base 3 of (2x+7) = 2

Sorry that I cannot show you any work, but frankly I am lost.

Use:

Log[sub:2ftdkzov]b[/sub:2ftdkzov](a[sup:2ftdkzov]m[/sup:2ftdkzov]) = m * Log[sub:2ftdkzov]b[/sub:2ftdkzov]a

and

Log[sub:2ftdkzov]b[/sub:2ftdkzov]a + Log[sub:2ftdkzov]b[/sub:2ftdkzov]c = Log[sub:2ftdkzov]b[/sub:2ftdkzov](a*c)

Now those properties have been refreshed - please show us your work.