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Do you know your basic logarithmic rules?
Alright well for the first one I would do Ln(1/2) ^x = ln15 then you can bring the exponent in front therefore giving you xln(1/2) = ln 15. Then you get x= ln (15) / ln(1/2)
for the second you have the rule of Log(a)b= c is the same as a^c = b

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Other answers:

ok..so how do i solve 2?
you have a ruole saying a√x = √b . Both a and b are constant. Therefore in this case you would have x =729 ending up as ( because what you do on the left you ahve to do on the right) 3 √x^3 =3√729 You should have a button on your calculator labelled as x√
err sorry I meant the rule is a√x^a = a√b
where the a's in : a√x^a cancel out. ( same as a square root and a square)
ok..
Do you understand or I made it too complicated?
kind of complicated..
alright I'll try to water it down. You know sqrt(x) = (x)^1/2 right? You have probably learned in algebra sqrt(x^2) ends up as X only because the sqrt cancels out with the square (^2) THEREFORE if you have x^3 = 729, you don't have an answer you WANT X= ? Therefore, you have to CANCEL OUT the ^3 somehow. The only way, like how you cancel a ^2 is by SQUARE ROOTING THE EXPRESSION so you end up with 3(sqrt)(x^3) = (x^3)^(1/3). By the rule of exponent, you multiplied the 2 of the ( 3*1/3) = 3/3 = 1 GIVING YOU X WHAT YOU DO ON THE LEFT YOU DO TO THE RIGHT THEREFORE (729)^(1/3) OR 3(sqrt)(729) the answer should be 9
I'm sorry if I made this too complicated, I just tried to explain the concept to it
perfectly fine..thank you Marc!
np

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