Log10y+2log10x=2,express y in terms of x
If log10y + 3log10x=2 express y in terms of x
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If that means log 'base 10' then,
log (y) + 2*log (x) = 2
Recall that we can rewrite the number that is multiplied by the the log expression as exponent of the term inside the log. For instance,
a * log (x) = log (x^a)
Thus,
log (y) + log (x^2) = 2
Recall that when log expressions with the same base are added, the terms inside the log can be multiplied and condensing everything to a single log. Thus,
log (y * x^2) = 2
We can raise 10 by both sides:
10^(log (y * x^2)) = 10^2
y * x^2 = 100
y = 100 / x^2
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To express y in terms of x using the given equation, we'll need to apply logarithmic properties and isolate y.
Given the equation: log10(y) + 2log10(x) = 2
We can use the logarithmic rule that states that logb(x^n) = nlogb(x). Applying this rule to the equation, we get:
log10(y) + log10(x^2) = 2
Using another logarithmic property, we can simplify the equation further:
log10(y * x^2) = 2
Now, we need to eliminate the logarithm on the left-hand side of the equation. To do this, we can express it in exponential form:
10^2 = y * x^2
Simplifying further:
100 = y * x^2
To express y in terms of x, divide both sides of the equation by x^2:
y = 100 / x^2
Therefore, y is equal to 100 divided by x squared.