Logarithms 4題

1.
logx^3 = log9x+2
3logx=log9+logx+2
2logx=log9+2
x^2=900
x=30or-30(reject)

2.
(3/4)^x =50
xlog(3/4)=log50
x=log50/log(3/4)
x=-13.6

3.
8^x=√30
xlog8=0.5log30
x=log30/(2log8)
x=0.818

4.
10^a+b=c
b=c-a^10
or
10^(a+b)=c
a+b=logc
b=logc-a

1.

logx^3 = log9x+2
3 logx = log 9x +2
log (x^3) - log 9x = 2
log (x^3 / 9x) =2
x^2 / 9 = 100
x^2 = 900
x = 30

2.

(3/4)^x =50
xlog(3/4) = log (100/2)
x (log 3 - 2log 2) = log 100 - log 2 = 2-log 2
x = ( 2-log 2 ) / (log 3 - 2log 2)


3.
8^x=√30
2^3x = 30 ^ 0.5
6x log 2 = log 30
x = (1/6) (log 30 / log 2)
x= (1/6) ((log 2 +log 3 + log 5) / log 2)
x= (1/6) (1+ (log 3/log 2) + (log 5/ log 2) )

4.
10^a+b = c
(a+b) log 10 = log c
a+b = log c
b = log c - a

1.
3logx = log9x + 2
3logx = log3^2 + logx + 2log10
2logx = 2log3 + 2log10
logx = log30
x = 30

2.
xlog(3/4) = log50
x = log50 / log(3/4)

3.
xlog8 = 0.5log30
x = log30 / 2log8 = log30 / log64

4.
b = c - 10^a

第四條有點牽強^^"
但是題目沒有要求應如何express