Solve for x over the real numbers:
5^((9 x)/2) = 625^(2 x-1)
Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
9/2 log(5) x = 4 log(5) (2 x-1)
Expand out terms of the right hand side:
9/2 log(5) x = 8 log(5) x-4 log(5)
Subtract 8 x log(5) from both sides:
-7/2 log(5) x = -4 log(5)
Divide both sides by -(7 log(5))/2:
Answer: |x = 8/7
+386 Can I have an in depth explanation for the following:
" Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
9/2 log(5) x = 4 log(5) (2 x-1) "
Take a good look at the line before that. What is it you don't understand?? If you have:
a^b=c^d, then take the log of both sides and you have:
b*log(a)=d*log(c). Do you get it?
+129840 (sqrt of 125)^3x = 625^(2x-1)
Tony, we can solve this one by equatiing bases.......notice that.....625 = 5^4
And sqrt of 125 can be wriiten as [125]^(1/2) = [ (5)^3]^(1/2) = 5^(3/2)
So we have
[ 5^(3/2) ] ^(3x) = [5^4 ] ^ (2x - 1) simplify
5^ [ ( 9/2 ) x] = 5^ [ 8x - 4]
Since we have the bases the same, we can just solve the exponential equations....so we have
(9/2)x = 8x - 4 multiply through by 2
9x = 16x - 8 add 8 to both sides and subtract 9x from both sides
8 = 7x divide both sides by 7
8 / 7 = x
