Question 328569
Two of your problems contain errors in typing so that we cannot help you
with them unless you repost and type them correctly.  I will do the ones 
which make sense.

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is this true or false:
{{{3log(b,(sqrt(3)))}}}{{{":"}}}{{{(a)=log(b,(a))}}}
<pre><b>
That one doesn't make any sense.  Why did you put a colon between the
expression on the left and the equation on the right?  

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</pre></b>
assume that x,y,z are positive numbers. use the properties of logarithms to write each expression as the logarithm of one quantity: 

{{{log(b,(x))+log(b,(x+2))-log(b,(8))}}}
<pre><b>
Use the logarithm identity {{{log(P,(Q))+log(P,(R))=log(P,(QR))}}} 

on the two highlighted terms below:

{{{highlight(log(b,(x))+log(b,(x+2)))-log(b,(8))}}}

{{{highlight(log(b,(x(x+2))))-log(b,(8))}}}

{{{log(b,(x(x+2)))-log(b,(8))}}}

Use the logarithm identity {{{log(P,(Q))-log(P,(R))=log(P,(Q/R))}}} on that:

{{{log(b,(x(x+2)/8))}}}

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</pre></b>
solve each equation. if answer not exact, give in four decimal places: 
{{{3^(x+3)=3^x=84}}} hint:{{{3^(x+3)=3^(x)(3)^3}}}
<pre><b>

That first equation has two equal signs.  One of them should have been either
a + or a - but I can't tell which one should have been which one.

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</pre></b>
write in terms of the logarithm x,y,and z: 

{{{log(b,(3xy))}}}
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Use the logarithm identity {{{log(P,(QRS))=log(P,(Q))+log(P,(R))+log(P,(S))}}} 

{{{log(b,(3xy))=log(b,(3))+log(b,(x))+log(b,(y))}}}

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write in terms of the logarithm x,y,and z: 

{{{drawing(120,80,0,1,-2,1,

locate(0,.2,
log(b,(x^(1/2)y^(3))))  ) }}}

Use the logarithm identity {{{log(P,(QR))=log(P,(Q))+log(P,(R))}}} 

{{{drawing(200,80,0,1,-2,1,

locate(0,.2,
log(b,(x^(1/2)))+log(b,(y^(3))))  ) }}}

Use the logarithm identity {{{log(P,(Q^R))=R*log(P,(Q))}}} on both terms:

{{{1/2}}}{{{log(b,(x))+3log(b,y)}}}

Edwin</pre>