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Im supposed to solve this equation using logarithms but I don't know how.

Im supposed to solve this equation using logarithms but I don't know how.-example-1
User PeterB
by
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1 Answer

9 votes

Given:


3(4^x)=5^(x+1)

To find:

The solution of the given equation.

Solution:

We have,


3(4^x)=5^(x+1)

It can be written as


3((2^2)^x)=5^(x+1)


3((2^(2x))=5^(x+1)
[\because (a^m)^n=a^(mn)]

Taking log on both sides.


\log [3((2^(2x))]=\log 5^(x+1)


\log 3+ \log ((2^(2x))=\log 5^(x+1)
[\because \log (ab)=\log a+\log b]


\log 3+ 2x\log 2=(x+1)\log 5
[\because \log x^n=n\log x]

Putting values of logarithms, we get


0.477+ 2x(0.301)=(x+1)0.699
[\because \log 2 =0.301, \log 3=0.477, \log 5=0.699]


0.477+ 0.602x=0.699x+0.699


0.602x-0.699x=0.699-0.477


-0.097x=0.222

Divide both sides by -0.097.


x=(0.222)/(-0.097)


x=-2.288656


x\approx -2.289

Therefore, the value of x is -2.289.

User Okliv
by
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