Question 563705
Let "b" be a number such that log(b)3 = 1.5 and log(b)5=2.2
evaluate the following:

1.  log (b)15
15 = 3*5
Multiplying --> adding the logs
{{{log(b,15) = log(b,3) + log(b,5) = 3.7}}}
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2.  log (b).6
0.6 = 3/5
Subtract logs when dividing
= log(3) - log(5) = -0.7
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3.  log (b)125
{{{125 = 5^3}}}
= 5*5*5
log(125) = log(5) + log(5) + log(5)
= 3*log(5)
Multiply the log by the exponent when raising to a power.
= 6.6
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4.  log (b)(^3sqrt(3))^7
If you mean {{{log(b,(root(3,3)^7))}}}
= {{{7*log(b,(root(3,3)))}}}  Multiply by the exponent

{{{root(3,3) = 3^(1/3)}}}
{{{log(3^(1/3)) = (1/3)*log(3) = 0.5}}} Multiply the log by the exponent
--> 7*0.5 = 3.5