document.write( "Question 560307: v=e^(w/pz)\r
\n" ); document.write( "\n" ); document.write( "Find w when v=15, p=1.2, z=34\r
\n" ); document.write( "\n" ); document.write( "i cant work out how to transpose this formula using logarithms to make part of the exponent (W) the subject.\r
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\n" ); document.write( "\n" ); document.write( "I=log(2,(1/p))\r
\n" ); document.write( "\n" ); document.write( "Find P when I=4\r
\n" ); document.write( "\n" ); document.write( "similar problem of being unable to separate the exponent to make it the subject \n" ); document.write( "
Algebra.Com's Answer #363822 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
your first problem is interpreted as follows:
\n" ); document.write( "the original equation i:
\n" ); document.write( "v=e^(w/pz)
\n" ); document.write( "Find w when v=15, p=1.2, z=34
\n" ); document.write( "substituting these values into your equation, you get:
\n" ); document.write( "15 = e^(w/(1.2*34)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "15 = e^(w/40.8)
\n" ); document.write( "take the natural log of both sides of this equation to get:
\n" ); document.write( "ln(15) = ln(e^(w/40.8)
\n" ); document.write( "note that ln means log to the base of e
\n" ); document.write( "example:
\n" ); document.write( "ln(x) means log of x to the base of e.
\n" ); document.write( "that could also be shown as log(e,x)
\n" ); document.write( "anyway, you take the natural log of both sides of the equation to get:
\n" ); document.write( "ln(15) = ln(e^(w/40.8)
\n" ); document.write( "by the rules of logarithms, log(x^y) = y * log(x)
\n" ); document.write( "in your equation, y = (w/40.8) and x = e and log = ln
\n" ); document.write( "using this rule, your equation becomes:
\n" ); document.write( "ln(15) = (w/40.8) * ln(e)
\n" ); document.write( "since ln(e) is equal to 1, your equation becomes:
\n" ); document.write( "ln(15) = (w/40.8)
\n" ); document.write( "multiply both sides of this equation by 40.8 to get:
\n" ); document.write( "w = ln(15) * 40.8
\n" ); document.write( "use your calculator to solve for w to get:
\n" ); document.write( "w = 110.4884482
\n" ); document.write( "substitute for w in your original equation to get:
\n" ); document.write( "original equation is:
\n" ); document.write( "v=e^(w/pz)
\n" ); document.write( "after substitution of all known values, equation becomes:
\n" ); document.write( "15 = e^(110.4884482/(1.2*34)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "15 = e^(110.4884482/40.8)
\n" ); document.write( "simplify further to get:
\n" ); document.write( "15 = e^(2.708050201)
\n" ); document.write( "simplify further to get:
\n" ); document.write( "15 = 15
\n" ); document.write( "this confirms the answer is good.
\n" ); document.write( "ln means natural log and is usually the LN function key on your calculator.
\n" ); document.write( "-----
\n" ); document.write( "my interpretation of your second problem equation is:
\n" ); document.write( "I=log(2,(1/p))
\n" ); document.write( "this means the log of (1/p) to the base of 2.
\n" ); document.write( "assuming this interpretation is correct, you would solve this as follows:
\n" ); document.write( "original equation is:
\n" ); document.write( "I = log(2,(1/p))
\n" ); document.write( "Find p when I=4
\n" ); document.write( "if your replace I with 4, then your equation becomes:
\n" ); document.write( "4 = log(2,(1/p))
\n" ); document.write( "in general, y = log(b,x) if and only if b^y = x
\n" ); document.write( "in your equation, b is equal to 2 and x is equal to (1/p) and y is equal to 4.
\n" ); document.write( "using this rule, your equation becomes:
\n" ); document.write( "4 = log(2,(1/p)) if and only if 2^4 = (1/p)
\n" ); document.write( "simplify this equation to get:
\n" ); document.write( "16 = (1/p)
\n" ); document.write( "multiply both sides of this equation by p to get:
\n" ); document.write( "16*p = 1
\n" ); document.write( "divide both sides of this equation by 16 to get:
\n" ); document.write( "p = 1/16
\n" ); document.write( "substitute for p in your original equation to see if it holds true.
\n" ); document.write( "your original equation is:
\n" ); document.write( "I=log(2,(1/p))
\n" ); document.write( "substitute 4 for I and (1/16) for p to get:
\n" ); document.write( "4 = log(2,(1/(1/16))
\n" ); document.write( "simplify this to get:
\n" ); document.write( "4 = log(2,16)
\n" ); document.write( "you can use your calculator to solve for log to the base of 2 as follows:
\n" ); document.write( "log(2,16) = log(16)/log(2)
\n" ); document.write( "your equation becomes:
\n" ); document.write( "4 = log(16)/log(2) which is simplified to:
\n" ); document.write( "4 = 3
\n" ); document.write( "this confirms the fact that p = (1/16) is a good value.\r
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