SOLUTION: Change from exponential form to logarithmic form and solve for x: 3^x-2=7 A)solve for x (exact solution) B)use calculator to solve for x and round to nearest thousandth Am

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Change from exponential form to logarithmic form and solve for x: 3^x-2=7 A)solve for x (exact solution) B)use calculator to solve for x and round to nearest thousandth Am      Log On


   



Question 432469: Change from exponential form to logarithmic form and solve for x:
3^x-2=7
A)solve for x (exact solution)
B)use calculator to solve for x and round to nearest thousandth
Am I doing this right?
A) log3 of 3^x-2=log3 of 7
x-2=log3 of 7 (+2 to both sides)
x=(log3 of 7)+2
x=(ln7/ln3)+2
Would this be my final answer for A?
B) Same steps as above
x=(ln7/ln3) +2
x=3.771 approximately rounded to the nearest thousandth
I just need to know if I am doing this correctly, and getting the correct solutions. If not I have to figure out where I am going wrong. Please guide me.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

your answer is correct...:-)
here is my version too:
—The Relationship—

y+=+bx

..............is equivalent to...............(means the exact same thing as)

logb%28y%29+=+x++

Change from exponential form to logarithmic form and solve for x:
3%5E%28x-2%29=7
A)solve for x+(exact solution)
B)use calculator to solve for x and round to nearest thousandth
y+=+bx ...................logb%28y%29+=+x+
y=3%5E%28x-2%29-7.............
y=3%5E%28x-2%29-7............ log%283%5E%28x-2%29%29+=+7
%28x-2%29ln%283%29+=+ln7+
x-2+=+ln7%2F+ln%283%29
x+=+ln7%2F++ln%283%29+%2B2
x+=+1.9459%2F++1.099+%2B2
x+=+1.9459%2F++1.099+%2B2=1.7706%2B2=3.771
3%5E3.771-2=7
3%5E1.771=7
6.998=7
7=7