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Solve the exponential equation below, fill in the blank if necessary

Solve the exponential equation below, fill in the blank if necessary-example-1
User Raghvendra Kumar
by
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1 Answer

26 votes
26 votes

Given:


((1)/(5))^x=6

Required:

We need to find the value of x.

Step-by-step explanation:

Taking log on both sides.


log((1)/(5))^x=log6
Use\text{ }log(a^x)=xlog(a).


xlog((1)/(5))=log6
Divide\text{ both sides of the equation by l}og((1)/(5))


x(log((1)/(5)))/(log((1)/(5)))=(log6)/(log((1)/(5)))


x=(log6)/(log((1)/(5)))


Use\text{ }log((a)/(b))=log(a)-log(b).


x=(log6)/(log(1)-log(5))


Use\text{ }log(1)=0.


x=(log6)/(-log(5))
x=-1.11328


x=-1.113

Final answer:


x=-1.113

User Sarim Sidd
by
3.2k points