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## Log expressions

Solve the following question:

An expression for y in terms of x by rearranging 18loge(x) = 6 - 3loge(y) is:

CAS is allowed.

Try to get y by itself by isolating the loge(y) term first: 3loge(y) = 6 - 18loge(x)

Divide both sides by 3: loge(y) = 2 - 6loge(x)

Now you can really just take "exponential" of both sides, which cancels the log and gets you y. For a cleaner solution though, let's manipulate the RHS a bit first:

$$\ln(y) = 2\ln(e) - 6\ln(x)$$

$$\ln(y) = \ln(e^2) - \ln(x^6)$$

$$\ln(y) = \ln\frac{e^2}{x^6}$$

$$y = \frac{e^2}{x^6}$$

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