Solve 4x+2 = 12 for x using the change of base formula

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