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Dmitry_Shevchenko [17]
3 years ago
11

Use logarithms to solve each equation 2x9/8=111

Mathematics
1 answer:
Illusion [34]3 years ago
7 0
<span>We have this equation:
</span>
2x^{\frac{9}{8}} = 111

and we need to find the value of x.

First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:

x^{\frac{9}{8}}=\frac{111}{2}
 
Next step we must do is to apply <span>logarithms:
</span>
logx^{\frac{9}{8}} = log(\frac{111}{2})

Next, we have to apply identities and then to solve the equation:

\frac{9}{8}logx = log(\frac{111}{2})
logx =  \frac{8}{9}log(\frac{111}{2})
logx = 1.5504
10^{logx} =  10^{1.5504}

Finally, we have the value of x which was our goal. This is the answer for the question above:

x= 35.5140

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