I understand how to do problems such as (2)(3^x)=(7)(5^x) but I'm stuck on these problems:
a) (4.6)(1.06^(2x+3))=(5)(3^x)
b) (2.67)(7.38^x)=(9.36^(5x-2))
c) (7)(0.43^(2x))=(9)(6^-x)
Any help would be greatly appreciated. Thanks.
You do them in the same way.
$\displaystyle ln \left ( 4.6 \cdot 1.06^{2x + 3} \right ) = ln \left ( 5 \cdot 3^x \right )$
(or you can take $\displaystyle log_a( )$ of both sides where a is your favorite base.)
$\displaystyle ln(4.6) + (2x + 3) \cdot ln(1.06) = ln(5) + x \cdot ln(3)$
which is just a linear equation for x. Solve for x.
-Dan
Taking it up from where I left off:
$\displaystyle 2~ln(1.06) \cdot x + 3 \cdot ln(1.06) + ln(4.6) = ln(3) \cdot x + ln(5)$
$\displaystyle (2~ln(1.06) - ln(3))x = ln(5) - 3 \cdot ln(1.06) - ln(4.6)$
$\displaystyle x = \frac{ln(5) - 3 \cdot ln(1.06) - ln(4.6)}{2~ln(1.06) - ln(3)} \approx 0.093094$
-Dan