Question

Solve 6x + 2 = 10 for x using the change of base formula log base b of y equals log y over log b.

Answer 1

Answer:

x= -0.715

Step-by-step explanation:

6^x+2 = 10

Step 1: Apply ln rule on both sides

ln rule: x^y = z

ln rule: (y)ln(x) = ln(z)

6^x+2 = 10

(x+2)*ln(6) = ln(10)

(x+2) = ln(10)/ln(6)

x+2 = 1.285

x = -0.715

Therefore, the right answer is the second option -0.715

!!

Answer 2

Answer:

The answer is -0.715

Step-by-step explanation:

Firstly, we use the change of base formula. The base must be 6 because the "x" variable is a power of it.

$6^x^+^2=10\\\\log_{6} (6^x^+^2)=log_{6} (10)$

Then, we can use the property logarithm power rule:

$log_{b}(x^y)=y* log_{b}(x)$

So,

$(x+2)*log_{6} (6)=log_{6} (10)\\log_{6} (6)=1\\x+2=log_{6} (10)\\\\log_{6} (10)=\frac{log(10)}{log(6)}\\log(10)=1\\\\x+2=\frac{1}{log(6)} \\x=\frac{1}{log(6)}-2$

Finally, the value of $\frac{1}{log(6)} =1.285$, therefore:

$x=1.285-2=-0.715$