From Förberedande kurs i matematik 1

Revision as of 13:22, 12 September 2008 (edit) Ian (Talk | contribs) ← Previous diff		Current revision (10:50, 2 October 2008) (edit) (undo) Tek (Talk | contribs) m
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-	The equation has the same form as the equation in exercise c and we can therefore use the same strategy.	+	The equation has the same form as the equation in exercise b and we can therefore use the same strategy.
	First, we take logs of both sides,		First, we take logs of both sides,
		+	{{Displayed math||<math>\ln\bigl(3e^x\bigr) = \ln\bigl(7\cdot 2^x\bigr)\,\textrm{,}</math>}}
-	<math>\ln \left( 3e^{x} \right)=\ln \left( 7\centerdot 2^{x} \right)</math>	+	and use the log laws to make <math>x</math> more accessible,
		+	{{Displayed math||<math>\ln 3 + x\cdot \ln e = \ln 7 + x\cdot \ln 2\,\textrm{.}</math>}}
-	and use the log laws to make	+	Then, collect together the <math>x</math> terms on the left-hand side,
-	<math>x</math>	+
-	more accessible:	+
-		+
-		+
-	<math>\ln 3+x\centerdot \ln e=\ln 7+x\centerdot \ln 2</math>	+
-		+
-		+
-	Then, collect together the <math>x</math> terms on the left-hand side:	+
-		+
-		+
-	<math>x\left( \ln e-\ln 2 \right)=\ln 7-\ln 3</math>	+
		+	{{Displayed math||<math>x(\ln e-\ln 2) = \ln 7-\ln 3\,\textrm{.}</math>}}
	The solution is now		The solution is now
-		+	{{Displayed math||<math>x = \frac{\ln 7-\ln 3}{\ln e-\ln 2} = \frac{\ln 7-\ln 3}{1-\ln 2}\,\textrm{.}</math>}}
-	<math>x=\frac{\ln 7-\ln 3}{\ln e-\ln 2}=\frac{\ln 7-\ln 3}{1-\ln 2}</math>	+

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Current revision

The equation has the same form as the equation in exercise b and we can therefore use the same strategy.

First, we take logs of both sides,

\displaystyle \ln\bigl(3e^x\bigr) = \ln\bigl(7\cdot 2^x\bigr)\,\textrm{,}

and use the log laws to make \displaystyle x more accessible,

\displaystyle \ln 3 + x\cdot \ln e = \ln 7 + x\cdot \ln 2\,\textrm{.}

Then, collect together the \displaystyle x terms on the left-hand side,

\displaystyle x(\ln e-\ln 2) = \ln 7-\ln 3\,\textrm{.}

The solution is now

\displaystyle x = \frac{\ln 7-\ln 3}{\ln e-\ln 2} = \frac{\ln 7-\ln 3}{1-\ln 2}\,\textrm{.}