128^(4x+1)+2 = 10

Question

please show all steps to get x alone. answer is -1/7

Answer 1

First step is to subtract 2 from both sides:

128^{(4x + 1)} = 8

Now, both 8 and 128 are powers of 2:
8 = 2³ and 128 = 2⁷

so we can replace these into our equation:

(2⁷)^{(4x + 1)} = 2³ 

When a base that is raised to a power is raised to another power, we can multiply the two exponents together and retain the base. This gives us:

(2)^{7(4x + 1)} = 2³   

Since we have the same base on both sides, we can just work with the exponents to get

7(4x + 1) = 3. Simplifying, we get

4x + 1 = 3/7

4x = -4/7

x = -4/28 = -1/7