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

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Answer 1 · 2016-06-17T08:13:49

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

#color(blue)(4) * 5 ^(x/2) = 500#

# 5 ^(x/2) = 500 / color(blue)(4#

# 5 ^(x/2) = 125#

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

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

#x/2 = 3#

#color(blue)(x = 6#