What is 2*10^{log_{2}(x)+log_{2}(x^2)} ?

The solution to 2*10^{log_{2}(x)+log_{2}(x^2)} is 2*1000^{log_{2}(x)}

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simplify 2*10^{log_{2}(x)+log_{2}(x^2)}

simplify

2 \cdot 1 0^{l o g_{2} (x) + l o g_{2} (x^{2})}

2 \cdot 100 0^{l o g_{2} (x)}

Solution steps

2 \cdot 1 0^{l o g_{2} (x) + l o g_{2} (x^{2})}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

1 0^{l o g_{2} (x) + l o g_{2} (x^{2})} = 1 0^{l o g_{2} (x)} \cdot 1 0^{l o g_{2} (x^{2})}

= 2 \cdot 1 0^{l o g_{2} (x)} \cdot 1 0^{l o g_{2} (x^{2})}

Simplify

1 0^{l o g_{2} (x^{2})} : 10 0^{l o g_{2} (x)}

= 2 \cdot 1 0^{l o g_{2} (x)} \cdot 10 0^{l o g_{2} (x)}

Apply exponent rule:

a^{n} b^{n} = (a \cdot b)^{n}

1 0^{l o g_{2} (x)} \cdot 10 0^{l o g_{2} (x)} = (10 \cdot 100)^{l o g_{2} (x)}

= 2 (10 \cdot 100)^{l o g_{2} (x)}

Multiply the numbers:

10 \cdot 100 = 1000

= 2 \cdot 100 0^{l o g_{2} (x)}

lo g_{2} (x) + lo g_{2} (3)

\frac{5}{2} ln (\frac{5}{2})

lo g_{10} (x y^{3})

lo g_{10} (z y^{9})

ln (\frac{x}{x - 10}) + ln (\frac{x + 10}{x}) - ln (x^{2} - 100)

What is 2*10^{log_{2}(x)+log_{2}(x^2)} ?
The solution to 2*10^{log_{2}(x)+log_{2}(x^2)} is 2*1000^{log_{2}(x)}