Question

Solve 5^(2x) = 7^(x−1). 1.52864 −1 −1.52864 1

Answer 1

$5^{2x}=7^{x-1}\\ \ln5^{2x}=\ln7^{x-1}\\ 2x \ln 5 =(x-1)\ln 7\\ 2x \ln 5 =x\ln 7-\ln 7\\ 2x\ln 5-x\ln 7=-\ln 7\\ x(2\ln5 -\ln 7)=-\ln7 \\ x=-\dfrac{\ln 7}{2\ln 5-\ln 7}\\ x\approx -1.52864$

Answer 2

Answer:

option C is correct.

Value of x = -1.52864

Step-by-step 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

$x = \frac{\ln 7}{\ln 7- 2\ln 5}$

Simplify:

x = -1.528643062439 ≈ - 1.52864

Therefore, value of x is, -1.52864