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:

  -0.715

Step-by-step explanation:

Take the log to the base 6, then apply your change-of-base formula.

  $6^{x+2}=10\\\\x+2=\log_6{10}\\\\x=\log_6{(10)}-2\\\\x=\dfrac{\log{10}}{\log{6}}-2\\\\x=\dfrac{1}{\log{6}}-2\approx -0.714903\\\\\boxed{x\approx -0.715}$