F.4logarithmic functions

21. 3(5^(2x-1))=2^(5x+1)
log3 + log (5^(2x-1)) = log2^(5x+1)
log3 + (2x-1)log5 = (5x+1)log2
log3 + (2log5)x - log5 = (5log2)x + log2
(2log5 - 5log2)x = log2 + log5 - log3
x = (log2 - log3 + log5) / (2log5 - 5log2) = -4.877146657
22.(5^(x+2))(7^x)=3
log(5^(x+2)) + log(7^x) = log3
(x+2)log5 + xlog7 = log3
(log5 + log7)x + 2log5 = log3
x = (log3 - 2log5) / (log5 + log7) = -0.596358921
23. 4^(x+2)-4^x=7
(4^2)(4^x) - 4^x = 7
(4^x) ( 4^2 - 1) = 7
log (4^x) + log15 = log7
log((2^2)^x) = log7 - log15
2xlog2 = log7 - log(3*5)
2xlog2 = log7 - log3 - log5
x = (log7 - log5 - log3) / (2log2) = -0.549767836
24. 3^(2x+1)+3^(2x-1)=8
3(3^2x) + (1/3)(3^2x) = 8
(3+ 1/3)(3^2x) = 8
log (3 + 1/3) + log (3^2x) = log8
log (10/3) + (2x)log3 = log (2^3)
(2x)log3 = 3log2 - (log10 - log3)
(2x)log3 = 3log2 - (1 - log3)
(2x)log3 = 3log2 + log3 - 1
x = (3log2 + log3 - 1) / (2log3) = 0.398442993