x^log x+5/3=10^5+log x
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HOMEWORK HELP > MATH
If log x^3- log 10x = log 10^5 find x
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HALA718 | CERTIFIED EDUCATOR
log x^3- log 10x = log 10^5
We will use logarithm properties to solve for x.
We know that log a - log b = log a/b
==> log x^3 - log 10x = log x^3/10x = log x^2/10
==> log x^2/10 = log 10^5
Now we have two equal logarithm with equal bases. Then, we conclude that the logs are equal.
==> x^2 /10 = 10^5
Now let us multiply both sides by 10.
==> x^2 = 10^5 * 10
We know that x^a * x^b = x^(a+ b)
==> x^2 = 10^(5+ 1)
==> x^2 = 10^6
Now we will re-write 10^6.
We know that 10^6 = 10^(2*3) = (10^3)^2.
==> x^2 = ( 10^3) ^2
Now we will take the root of both sides.
==> x = 10^3= 1000
==> Then, the answer is x = 1000.
HOMEWORK HELP > MATH
If log x^3- log 10x = log 10^5 find x
print Print document PDF list Cite
Expert Answers
HALA718 | CERTIFIED EDUCATOR
log x^3- log 10x = log 10^5
We will use logarithm properties to solve for x.
We know that log a - log b = log a/b
==> log x^3 - log 10x = log x^3/10x = log x^2/10
==> log x^2/10 = log 10^5
Now we have two equal logarithm with equal bases. Then, we conclude that the logs are equal.
==> x^2 /10 = 10^5
Now let us multiply both sides by 10.
==> x^2 = 10^5 * 10
We know that x^a * x^b = x^(a+ b)
==> x^2 = 10^(5+ 1)
==> x^2 = 10^6
Now we will re-write 10^6.
We know that 10^6 = 10^(2*3) = (10^3)^2.
==> x^2 = ( 10^3) ^2
Now we will take the root of both sides.
==> x = 10^3= 1000
==> Then, the answer is x = 1000.
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