Question 563670
This is just making use of general rules of logs:
(1) {{{ log(a*b) = log(a) + log(b) }}}
(2) {{{ log(a/b) = log(a)  - log(b) }}}
(3) {{{ log(a^b) = b*log(a) }}}
(4) {{{ log(b,b) = 1 }}}
All these rules can use any base for the logs
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{{{ log( b,3 ) = 1.5 }}}
{{{ log( b,5 ) = 2.2 }}}
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(1)
{{{ log( b,5/3 ) = log( b,5 ) - log( b,3 ) }}}
{{{ log( b,5/3 ) = 2.2 - 1.5 }}}
{{{ log( b,5/3 ) = .7 }}}
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(2)
{{{ log( b,3b^2 ) = log(b,3) + 2*log(b,b) }}}
{{{ log( b,3b^2 ) = 1.5 + 2*1 }}}
{{{ log( b,3b^2 ) = 3.5 }}}
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(3)
{{{ log( b,45 ) = log(b,9) + log(b,5) }}}
{{{ log( b,45 ) = log(b,3^2) + 2.2 }}}
{{{ log( b,45 ) = 2*log(b,3) + 2.2 }}}
{{{ log( b,45 ) = 2*1.5 + 2.2 }}}
{{{ log( b,45 ) = 5.2 }}}
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(4)
{{{ log( b,b/15 ) = log( b,b ) - log( b,15 ) }}}
{{{ log( b,b/15 ) = 1 - log( b,3*5 ) }}}
{{{ log( b,b/15 ) = 1 - log( b,3 ) - log( b,5 ) }}}
{{{ log( b,b/15 ) = 1 - 1.5 - 2.2 }}}
{{{ log( b,b/15 ) = 1 - 3.7 }}}
{{{ log( b,b/15 ) = -2.7 }}}