HElp Logarithmic functions (1 Viewer)

[starbuckscoffee]

1. Solve the equation log5 x= 16logx 5

2. Gven that q^p =25, find log5q in terms of p

Thanks

 

[Slidey]

1) use change of base:
log_5(x)=16log_x(5), so
ln(x)/ln5=16ln5/lnx
ln(x)^2=(4ln5)^2
ln(x)^2=(ln625)^2
x=625 or 5^4

2) take the log_5 of both sides:
p*log_5(q)=2
log_5(q)=2/p

 

[lanvins]

More questions,

1.a If a log2 7= 3- log6 14, find the value of a, correct to three significant figures

b. If log3 18= log11 k, find the value of k, correct to one decemial place

2. Solve- 3^(2x) - 3^(x+2)+8=0

Thanks

 

[Slidey]

1a) use change of base then use the rule that lna+lnb=ln(ab), now apply your slide rule and log tables. Alternatively, since you have a calculator, a=(3-log_6(14))/log_2(7)
b) Use change of base, then log laws, then isolate log_whatever(k) and raise both sides to the power of the base you picked.

2) It's a quadratic in 3^x.
3^(2x) - 3^2*3^x + 8 = 0
let y=3^x
y^2-9y+8=0
y=1, 9
Thus x=0, 2

 

[Slidey]

haha

You know my name on here was originally Slide Rule?