log_0.1 to x=4log_0.1 to 3 - 2/3log_0.1 to 27+2log_0.1 to 6?

Taking the antilog, you have

.. x = 3^4/27^(2/3)*6^2

.. = 4*3^6/3^2

.. = 3^4/3^2*6^2

.. = 9*36

.. = 324

We say "log OF", not "log to"

log_0.1(x) = 4 log_0.1(3) − 2/3 log_0.1(27) + 2 log_0.1(6)

log_0.1(x) = log_0.1(3^4) − log_0.1(27^(2/3)) + log_0.1(6^2)

log_0.1(x) = log_0.1(81) − log_0.1(9) + log_0.1(36)

log_0.1(x) = log_0.1(81/9*36)

log_0.1(x) = log_0.1(324)

x = 324

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