Solving 2^x=7*5^x: Tips & Tricks

  • Thread starter chjopl
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In summary, to solve the equation 2^x=7*5^x, take the natural logarithm of both sides and use the property ln(ab)=ln(a)+ln(b). This will result in x=\frac{\ln 7}{\ln 2-\ln 5}. It is important to remember to take the natural logarithm of both sides and not just one side.
  • #1
chjopl
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2^x=7*5^x
I know you have to take ln of both sides but i am having trouble doing that for the right side.
 
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  • #2
Remember the property of logarithms, ln(ab)=ln(a)+ln(b). That should help you deal with the right hand side.
 
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  • #3
chjopl said:
2^x=7*5^x
I know you have to take ln of both sides but i am having trouble doing that for the right side.

I could give u the only hint possible,but that would be useless.So i'll better show u my version.Logarithmate both sides of the equation to find:
[tex] x\ln 2=\ln 7+x\ln 5 =>x=\frac{\ln 7}{\ln 2-\ln 5} [/tex].

Okay...??Clear?

PS:Shmoe,u were quicker than me...Again. :tongue2:
 
  • #4
Yeah thanks a lot i was messing up and having ln7*xln5
 

Q1: What is the first step in solving 2^x=7*5^x?

The first step in solving this equation is to rewrite it as 2^x = 7^(1-x).

Q2: What is the most common mistake when solving this type of equation?

The most common mistake is forgetting to distribute the exponent of x to both 7 and 5, resulting in an incorrect solution.

Q3: How can I simplify the equation 2^x=7*5^x before solving?

You can simplify this equation by dividing both sides by 5^x, resulting in 2^(x-x)=7, which simplifies to 2^0=7, or 1=7. Since this is not a true statement, there is no solution.

Q4: Are there any special cases or restrictions when solving this type of equation?

Yes, there are restrictions when the bases of the exponents are equal. In this case, the equation would simplify to 2^x=7*2^x, which has no solution. This is because the bases must be different in order for the equation to be solvable.

Q5: Can I use logarithms to solve this equation?

Yes, you can use logarithms to solve this equation. Taking the logarithm of both sides will result in x*log2 = log7 + x*log5. You can then rearrange the equation to solve for x.

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