Can someone please explain how to solve one or 2 of these exponential equations? Thanks!
To solve exponential equation, it is better if we can express each side with the same base.
Then, simplify the right side by applying the exponent rule `(a^m)^n = a^(m*n)` .
Now that each side have the same base, set the exponents equal to each other.
`x-4=2x - 12`
And, isolate the x.
Hence, the solution is x = 8.
Factor 49 to see if both if both sides can be expres with same base.
Since they can both be express with same base, to solve, set their exponents equal to each other.
`3x +4=4x + 2`
And, isolate x.
Thus, the solution is x=2.
6) `27^(4x-1) = 9^(3x+8)`
The trick for this problem is to recognize that 27 = 9^(3/2).
`(9^(3/2))^(4x-1) = 9^(3x+8)`
Using the exponent rule we can simplify
`9^(6x - 3/2) = 9^(3x+8)`
Now we set the exponents equal to each other because they have the same base.
`6x - 3/2 = 3x + 8`
`x = 19/6`
Here we need to recognize that 64 = 4^3
`4^(2x-5) = (4^3)^(3x)`
`4^(2x-5) = 4^(9x)`
`2x - 5 = 9x`
`-5 = 7x`
`-5/7 = x`