SOLUTION: Can someone please help!!! Round to four decimal places if necessary. 1. (1/5)^t-2=125 2. log4(x-9)=2 3. log4z+log4(z-3)=1 4. 3.9^m-4=10.21 I have to show my work and th

Question 167590: Can someone please help!!!
Round to four decimal places if necessary.
1. (1/5)^t-2=125
2. log4(x-9)=2
3. log4z+log4(z-3)=1
4. 3.9^m-4=10.21
I have to show my work and these I don't understand how to do.
Thanks
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
This site provides "log rules":
http://www.purplemath.com/modules/logrules.htm
You will need to apply them to your problems.
.
1. (1/5)^t-2=125
take the log base 1/5 of both sides
t-2 = log(125)/log(1/5)
t-2 = 2.09691/-0.9542
t-2 = -2.1975
t = -0.1975
.
2. log4(x-9)=2
x-9 = 4^2
x-9 = 16
x = 25
.
3. log4z+log4(z-3)=1
the above is equivalent to:
log4[z(z-3)]=1
z(z-3)=4^1
z(z-3)=4
z^2-3z = 4
z^2-3z-4 = 0
(z-4)(z+1) = 0
z = {-1,4}
.
4. 3.9^m-4=10.21
m-4 = log(10.21)/log(3.9)
m-4 = 1.7071
m = 5.7071

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