Question 1129238
Solve the equation by rewriting the exponential expressions using the indicated logarithm.

e^4x = 19 using the natural log

60^e−0.12t = 10 using the natural log

*Knowing that the natural log base is 10 the answers that I came up with was: log10=19, but I don't know where the 4 is suppose to go. The same confusion goes for the second one, I thought the equation should be set up as log10=10, but I don't know where 60 and e^-0.12t goes. Can someone explain how to properly set up the equation? Thanks. 
<pre>a)  If it's {{{matrix(1,3, e^(4x), "=", 19)}}}, then:
{{{matrix(1,3, 4x, "=", ln (19))}}} ----- Converting to NATURAL LOGARITHMIC (ln) form
{{{highlight_green(matrix(1,5, x, "=", ln (19)/4, "=", 0.736109745))}}}

b)  If it's {{{matrix(1,3, 60^(e - .12t), "=", 10)}}}, then:
{{{matrix(1,3, ln (60^(e - .12t)), "=", ln (10))}}} ----- Taking the NATURAL LOG (ln) of each side
{{{matrix(1,3, (e - .12t) * ln (60), "=", ln (10))}}}
{{{matrix(1,3, e - .12t, "=", ln (10)/ln (60))}}}
{{{matrix(1,3, - .12t, "=", ln (10)/ln (60) - e)}}}
{{{highlight(highlight_green(highlight(matrix(1,5, t, "=", (ln (10)/ln (60) - e)/(- .12), "=", 17.96583311))))}}}

OR

b)  If it's {{{matrix(1,3, 60^e - .12t, "=", 10)}}}, then you DO NOT NEED to use REGULAR or NATURAL LOGS to solve. Do as follows:
{{{matrix(1,3, - .12t, "=", 10 - 60^e)}}}
{{{highlight(highlight_green(highlight(matrix(1,5, t, "=", (10 - 60^e)/(- .12), "=", 567899.2074))))}}}
That's ALL!!