Question

Solve the linear equation frac%7B3%7D%7B4%7D%29%5E%7Bx-7%7D" id="TexFormula1" title="(\frac{16}{9})^{-2x+5} = (\frac{3}{4})^{x-7}" alt="(\frac{16}{9})^{-2x+5} = (\frac{3}{4})^{x-7}" align="absmiddle" class="latex-formula">

Answer 1

Graph both equations and find the X value when the lines cross.

See attached picture of the graph

X = 1

Or you could take logarithms of both sides where log(a^b) = b loga to also find the value of x.

Answer 2

Answer:

x = 1

Step-by-step explanation:

Given in the question,

$(16/9)^{-2x+5} = (3/4)^{(x-7)}$

Take logarithm on both sides

$ln(16/9)^{-2x+5} = ln(3/4)^{(x-7)}$

Apply power rule of logarithm

(-2x+5)ln(16/9) = (x-7)ln(3/4)

cross multiply

(-2x+5)/(x-7) = $\frac{ln(3/4)}{ln(16/9)}$

-1/2 = (-2x+5)/(x-7)

-(x-7) = 2(-2x+5)

-x + 7 = -4x + 10

rearrange the terms, x terms to left and constant to right

-x + 4x = 10 - 7

3x = 3

x = 1