Pre Calc ?? dealing w logs and exponets and all that good stuff.?

Question

can any one solve 6^(2x)=90 and show me how thanks

Answer 1

First convert the eqn into log format:

log_6 90 = 2x

Now rewrite the log by using change of base:

log 90 / log 6 = 2x

Now divide by 2 to get:

log 90 / (2 log 6) = x

which is about 1.256

Answer 2

The trick is to make sure you have the same base.

To convert 90 with a base of 6 , the equation is 6^y = 90

y is the exponent to which the base six must be raised to get 90.

A little estimation tells you it is between 6^2 = 36 and 6^3 = 216. So expect an exponent in between 2 and 3.

using your calculator, evaluate y = log 90/log 6 = 2.51139...

then, 6^2x = 6^2.51139

or 2x = 2.51139

x = 1.2556....

or just using the rules of logs. 6^2x = 2x log 6

2x log 6 = log 90
solving for x you get the same value.