Math Doubts
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Math Doubts
4M ago
$=\,\,$ $64 \times x^3+1$
$=\,\,$ $4 \times 16 \times x^3+1$
$=\,\,$ $4 \times 4 \times 4 \times x^3+1$
$=\,\,$ $4^3 \times x^3+1$
$=\,\,$ $(4 \times x)^3+1$
$=\,\,$ $(4x)^3+1$
$=\,\,$ $(4x)^3+1 \times 1 \times 1$
$=\,\,$ $(4x)^3+1^3 ..read more
Math Doubts
4M ago
The subtraction of sixteen from the square of $x$ is an algebraic expression and it should be factorized in this algebraic question. So, let’s learn how to factorize the algebraic expression $x$ square minus sixteen in this math problem.
Check the possibility expressing it in square form
$\implies$ $x^2-16$ $=\,\,$ $x^2-4 \times 4$
$=\,\,$ $x^2-4^2$
Check the possibility expressing it in square form
$\implies$ $x^2-4^2$ $\,=\,$ $(x+4)(x-4 ..read more
Math Doubts
4M ago
$=\,\,$ $\displaystyle \int{\sin^2{x}}\,dx$
$=\,\,$ $\displaystyle \int{\dfrac{1+\cos{2x}}{2}}\,dx$
$=\,\,$ $\displaystyle \int{\bigg(\dfrac{1}{2}+\dfrac{\cos{2x}}{2}\bigg)}\,dx$
$=\,\,$ $\displaystyle \int{\dfrac{1}{2}}\,dx$ $+$ $\displaystyle \int{\dfrac{\cos{2x}}{2}}\,dx$
$=\,\,$ $\displaystyle \int{\Big(\dfrac{1}{2} \times \Big)}\,dx$ $+$ $\displaystyle \int{\Big(\dfrac{1 \times \cos{2x}}{2}\Big)}\,dx ..read more
Math Doubts
8M ago
$=\,\,$ $\displaystyle \int{\dfrac{1}{\sqrt{x+1}-\sqrt[\Large 4]{x+1}}}\,dx$
$=\,\,$ $\displaystyle \int{\dfrac{1}{(x+1)^{\Large \frac{1}{2}}-(x+1)^{\Large \frac{1}{4}}}}\,dx$
$\implies$ $\displaystyle \int{\dfrac{1}{(x+1)^{\Large \frac{1}{2}}-(x+1)^{\Large \frac{1}{4}}}}\,dx$ $\,=\,$ $\displaystyle \int{\dfrac{1}{(y^4)^{\Large \frac{1}{2}}-(y^4)^{\Large \frac{1}{4}}}}\,(4y^3dy)$
$=\,\,$ $\displaystyle \int{\dfrac{1}{(y^4)^{\Large \frac{1}{2}}-(y^4)^{\Large \frac{1}{4}}}}\,(4y^3dy)$
$=\,\,$ $\displaystyle \int{\dfrac{1}{(y^4)^{\Large \frac{1}{2}}-(y^4)^{\Large \frac{1}{4}}}}\,\times 4y^3 \time ..read more
Math Doubts
9M ago
It is given in this problem that $(2.3)^{\displaystyle x} = (0.23)^{\displaystyle y} = 1000$.
Step: 1
Consider $(2.3)^{\displaystyle x} = 1000$
The value of the right hand side of this equation is $1000$ and it can be written as the factors of $10$. So, take the common logarithm both sides.
$\implies \log (2.3)^{\displaystyle x} = \log 1000$
$\implies \log (2.3)^{\displaystyle x} = \log 10^3$
Use power rule of logarithm.
$\implies x \log 2.3 = 3 \log 10$
The base of the common logarithm is $10$. So, the $\log 10 = 1$.
$\implies x \log 2.3 = 3 \times 1$
$\implies x \log 2.3 = 3$
$\implies \log ..read more