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

1 Answer
Jun 17, 2016

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

Explanation:

#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#