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andrew11 [14]
3 years ago
7

What is equal to 3log2 + log4

Mathematics
2 answers:
Sunny_sXe [5.5K]3 years ago
7 0
Well I tried sloving it and I got 1.5
sineoko [7]3 years ago
4 0
Log Rule #1:  log(x*y) = log(x)+log(y)
Log Rule #2:  log(x^y) = y*log(x)

Using those log rules, we can say...

3*log(2) + log(4) = log(2^3) + log(4)  <-- use log rule #2
3*log(2) + log(4) = log(8) + log(4)     <-- simplify 2^3 to get 8
3*log(2) + log(4) = log(8*4)               <-- use log rule #1
3*log(2) + log(4) = log(32)                <-- simplify 8*4 to get 32

So the expression simplifies to log(32)
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The diagonals of a rhombus measures 6cm and 8cm, what is the perimeter of this rhombus?
Kamila [148]
<h2><u>Diagram</u><u>:</u><u>-</u></h2>

\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4)\qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}

<h3><u>Required Answer</u><u>:</u><u>-</u></h3>

The diagonals of the Rhombus= d1 & d2=6cm and 8cm

Let the Side=a

As we know that in a Rhombus

{\boxed{\sf side=\sqrt {\left ({\dfrac{d1}{2}}\right)^2+\left ({\dfrac {d2}{2}}\right)^2}}}

  • Substitute the values

{:}\longmapsto\sf a=\sqrt {\left ({\dfrac {6}{2}}\right)^2+\left ({\dfrac {8}{2}}\right)^2 }

{:}\longmapsto\sf a=\sqrt {(3)^2+(4)^2}

{:}\longmapsto\sf a=\sqrt {9+16}

{:}\longmapsto\sf a=\sqrt{25}

{:}\longmapsto\sf a=5cm

<h2>_____________</h2><h3>Again </h3>

we know that in a Rhombus

\boxed{\sf Perimeter=4a}

  • Substitute the values

{:}\longmapsto\sf Perimeter=4×5

{:}\longmapsto\sf Perimeter=20cm

\thereforePerimeter of the rectangle is 20cm.

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ivanzaharov [21]
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