Question

Solve 5^(2x) = 7^(x−1).

1.52864
−1
−1.52864
1

Answer 1

`5^(2x)=7^(x-1)\\ \ln5^(2x)=\ln7^(x-1)\\ 2x \ln 5 =(x-1)\ln 7\\ 2x \ln 5 =x\ln 7-\ln 7\\ 2x\ln 5-x\ln 7=-\ln 7\\ x(2\ln5 -\ln 7)=-\ln7 \\ x=-(\ln 7)/(2\ln 5-\ln 7)\\ x\approx -1.52864`

Answer 2

option C is correct.

Value of x = -1.52864

Explanation:

Solve:
`5^(2x) = 7^(x-1)` .....[1]

Using logarithmic rule:

`\ln a^n = n \ln a`

Taking log with base e both sides in [1] we get;

`\ln 5^(2x) = \ln 7^(x-1)`

Apply logarithmic rules; we have

`2x \ln 5 = (x-1) \ln 7`

Using distributive property:
`a \cdot ( b+c) = a\cdot b + a\cdot c`

`2x \ln 5 = x\ln 7-\ln 7`

Add both sides
`\ln 7` we get;

`2x \ln 5 +\ln 7= x\ln 7`

or

`\ln 7= x\ln 7-2x \ln 5`

`\ln 7= x(\ln 7-2\ln 5)`

or

`x = (\ln 7)/(\ln 7- 2\ln 5)`

Simplify:

x = -1.528643062439 ≈ - 1.52864

Therefore, value of x is, -1.52864