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klasskru [66]
3 years ago
5

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

Mathematics
2 answers:
marusya05 [52]3 years ago
4 0

Answer:

x= -0.715

Step-by-step explanation:

6^x+2 = 10

<u>Step 1: Apply ln rule on both sides</u>

ln rule: x^y = z

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

<em>6^x+2 = 10</em>

<em>(x+2)*ln(6) = ln(10)</em>

<em>(x+2) = ln(10)/ln(6)</em>

<em>x+2 = 1.285</em>

x = -0.715

Therefore, the right answer is the second option -0.715

!!

kodGreya [7K]3 years ago
3 0

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

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