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How would i find x in the equation: 14^x=91

 Mar 26, 2015

Best Answer 

 #2
avatar+26364 
+10

14^x=91

$$\small{\text{
$
\begin{array}{rcl}
14^x &=& 91 \quad | \quad \ln() \\
\ln(14^x) &=& \ln(91) \\
x\cdot \ln(14) &=& \ln(91) \\\\
x &=& \dfrac{\ln(91)} { \ln(14)} \\\\
x &=& \dfrac{4.51085950652} { 0.32220425047} \\\\
x &=& 1.70926923637
\end{array}
$
}}$$

$$14^{1.70926923637} = 91$$

 

or

$$\small{\text{
$
\begin{array}{rcl}
14\cdot x &=& 91 \\\\
x = \dfrac{91}{14} \\\\
x = 6.5
\end{array}
$
}}$$

$$14\cdot 6.5= 91$$

 Mar 26, 2015
 #1
avatar
0

My teacher taught us to guess and check.. 14*14=?*14=? until you get 91.

 Mar 26, 2015
 #2
avatar+26364 
+10
Best Answer

14^x=91

$$\small{\text{
$
\begin{array}{rcl}
14^x &=& 91 \quad | \quad \ln() \\
\ln(14^x) &=& \ln(91) \\
x\cdot \ln(14) &=& \ln(91) \\\\
x &=& \dfrac{\ln(91)} { \ln(14)} \\\\
x &=& \dfrac{4.51085950652} { 0.32220425047} \\\\
x &=& 1.70926923637
\end{array}
$
}}$$

$$14^{1.70926923637} = 91$$

 

or

$$\small{\text{
$
\begin{array}{rcl}
14\cdot x &=& 91 \\\\
x = \dfrac{91}{14} \\\\
x = 6.5
\end{array}
$
}}$$

$$14\cdot 6.5= 91$$

heureka Mar 26, 2015

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