Question 1028824
(a) 
{{{ 3^(2n + 1 ) = 81 }}}
{{{ 3^( 2n + 1 ) = 3^4 }}}
{{{ 2n + 1 = 4 }}}
{{{ 2n = 3 }}}
{{{ n = 3/2 }}}
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check:

{{{ 3^((2*(3/2)) + 1 ) = 81 }}}
{{{ 3^4 = 81 }}}
{{{ 81 = 81 }}}
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(b)
{{{ log(4) + log( z+3 ) = 2 }}}
( whenever the base is not specified,
it is assumed to be 10 )
{{{ log( 4*( z+3 ) ) = 2 }}}
Now the trick is to express {{{ 2 }}} as a log
{{{ log( 4*( z+3 ) ) = log( 100 ) }}}
{{{ 4*( z+3 ) = 100 }}}
{{{ 4z + 12 = 100 }}}
{{{ 4z = 88 }}}
{{{ z = 22 }}}
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check:
{{{ log(4) + log( z+3 ) = 2 }}}
{{{ log(4) + log( 22+3 ) = 2 }}}
{{{ log(4) + log(25) = 2 }}}
{{{ .60206 + 1.39794 = 2 }}}
{{{ 2 = 2 }}}
OK