# exponential equations

I'm looking for exponential equations that require the application of the properties of logarithms and can be solved without a calculator (by evaluating the logarithm).

example: 27 = 3^(5x) . 9^(x^2^x)

The example is the one exercise I've found so far.

Any ideas where I could find problems like that?

• second result on google for "logarithm exercises": oxfordmathcenter.com/drupal7/node/533 At first glance, I'd say at least half of these can be done without calculator. – Dirk Liebhold Aug 2 at 7:19
• I would just take any equation that they know how to solve and exponentiate it to a base of my choosing to get a broad selection of problems. (Maybe do some manipulations like expansion of sums in the exponent to products.) However, how do you expect students to deal with the 9^(x^2^x) term? Also, do you mean $9^{(x^2)^x}$ or $9^{x^{2^x}}$? They are not the same. – Adam Aug 2 at 13:36