How do you solve $4 \cdot 5^{\frac{x}{2}} = 500$ $4*5^(x/2)=500$ ?

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Answer 1 · 2016-06-17T08:13:49

The value of $x = 6$ $color(blue)(x = 6$

$4 \cdot 5^{\frac{x}{2}} = 500$ $color(blue)(4) * 5 ^(x/2) = 500$

$5^{\frac{x}{2}} = \frac{500}{4}$ $5 ^(x/2) = 500 / color(blue)(4$

$5^{\frac{x}{2}} = 125$ $5 ^(x/2) = 125$

$125$ $125$ can also be expressed as $5^{3}$ $5^3$ , so the expression now becomes:

$5^{\frac{x}{2}} = 5^{3}$ $5 ^(x/2) = 5^3$
Now as the bases are equal we can equate the powers and obtain the value of $x .$ $x.$

$\frac{x}{2} = 3$ $x/2 = 3$

$x = 6$ $color(blue)(x = 6$

How do you solve 4⋅5x2=5004*5^(x/2)=500?