The expression ( \log \left( \frac{x^2 \cdot y^3}{z^4} \right) ) can be simplified using logarithmic properties. It can be rewritten as ( \log(x^2) + \log(y^3) - \log(z^4) ). Further simplifying each term gives ( 2 \log(x) + 3 \log(y) - 4 \log(z) ). Thus, the final expression is ( 2 \log(x) + 3 \log(y) - 4 \log(z) ).
x2-8x=0 ( add 8x to both sides) x2 =8x (divide by x) x=8 ( x2divided by x equals x)
6
If you have like terms then to multiply you add the exponents and to divide you subtract.So, x2 * x3 = x5 and y7 / y5 = y2Also, for example, 2x2 * x3 = 2x5 (we can do this as the terms are like; x's only)But if you do not have like terms then this does not apply.For example, x2 * y3 does not equal xy5.
2x2 + x2 = 3x2
Only if x is equal to 2.
log(9x) + log(x) = 4log(10)log(9) + log(x) + log(x) = 4log(10)2log(x) = 4log(10) - log(9)log(x2) = log(104) - log(9)log(x2) = log(104/9)x2 = 104/9x = 102/3x = 33 and 1/3
x2-8x=0 ( add 8x to both sides) x2 =8x (divide by x) x=8 ( x2divided by x equals x)
6
0
x3-x2 Both terms in this expression have x2 in them, so "divide" each term by it using the distributive property in reverse. x2(x-1) = x3-x2 If you "re-distribute" you should see that they are equal.
2 log(x) = log(8)log(x2) = log(8)x2 = 8x = sqrt(8) = 2.82843 (rounded)Note that only the positive square root of 8 can serve as a solution to thegiven equation, since there's no such thing as the log of a negative number.
5
11-x2=-5 add -11 to both sides: 11-x2-11=-5-11 -x2=-16 divide both sides by -2: (-x2)/(-2)=(-16)/(-2) x=8 If the "x2" was supposed to be "x2", meaning exponentiation, ("x squared") and not "x2", implying multiplication, ("x times two") then we'd get: x2=16 x=±4
If you have like terms then to multiply you add the exponents and to divide you subtract.So, x2 * x3 = x5 and y7 / y5 = y2Also, for example, 2x2 * x3 = 2x5 (we can do this as the terms are like; x's only)But if you do not have like terms then this does not apply.For example, x2 * y3 does not equal xy5.
2x2 + x2 = 3x2
It equals x2 - 34
log x2 = 2 is the same as 2 log x = 2 (from the properties of logarithms), and this is true for x = 10, because log x2 = 2 2 log x = 2 log x = 1 log10 x = 1 x = 101 x = 10 (check)