Question

Solve 4x+2 = 12 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

The answer is 3.5
You can just stick with a 2 step equation method and it would work.

Answer 2

Answer:

$x=2.5$

Step-by-step explanation:

We have,

$4x+2=12$

$\implies4x=10$

Taking log both the sides we have,  

$log\,4x=log\,10$

$\implies log\,4 + log\,x=log\,10 \left\:\: [ \because log\,ab = log\, a + log\, b\right ]$

$\implies log\,x=log\,10 -log\,4$

$\implies log\,x={ log\,(\frac{10}{4}) \:\:\left [\because log\,a -log\,b= log\,\frac{a}{b} \right ]$

$\implies log\,x=log\,2.5$

$\implies \frac{log\,x}{log\,2.5}=1$

$\implies log_{(2.5)}\, x=1\:\:\left [ \because log_{b}\,a=\frac{log\,a}{log\,b} \right ]$

$\implies x=(2.5)^{1}\:\: [ \because log_{b}\,a=m \implies a=b^{m} ]$

Hence, we have $x=2.5$