Please show all work. Solve using logarithms!
6 Answers

Solve for x, add log to each side: log (1/16) = log 64^(4x – 3)
Property of log, move exponent to coefficient: log (1/16) = (4x – 3) * log 64
Divide log 64 to each side: log (1/16) / log 64 = 4x – 3
Simplify: (2/3) = 4x – 3
Add 3 to each side: 3 – (2/3) = 4x
Common denominator: (9 – 2) / 3 = 4x
Simplify: 7 / 3 = 4x
Divide 4 to each side: x = 7/12

log (1/16) = (4*x – 3)*log 64
– log 16 = (4*x – 3)*log 64
4*x – 3 = (log 16/log 64)
= – log 2^4 / log 2^6
= – 4*log 2/ 6*log 2 = – 2/3
4*x – 3 = 2/3
4*x = 9/3 – 2/3 = 7/3
x = 7/12 <<<

log (1/16) = (4x – 3) log 64
– 2 = 3 (4x – 3) <———taking log base as 4
– 2 = 12x – 9
12x = 7
x = 7/12

1/16 = 64^(4x3)
log(1/16) = log(64^(4x3))
log(16) = (4x3) log(64)
log(2^4) = (4x3) log(2^6)
4 log(2) = (4x3) 6 log(2)
4 = (4x – 3) 6
4 = 24x – 18
24x = 14
x = 14/24 = 7/12

1/16 log (base 64) = 4x – 3
log (1/16) / log(64) = 4x – 3
4x – 3 = 2/3
4x = 7/3
x = 7/12

2^x = 30 log 2^x = log 30 <– Take log of the two component x log2 = log 30 <– Rule : log a^x = xloga x = log 30/log 2 5^(x – a million) = 3^x log 5^(xa million) = log 3 ^x (xa million) log5 = x log 3 xlog5 log 5 = xlog3 xlog5 xlog3 = log 5 x(log5 log3) = log 5 x = log5/(log5log3) 3.5^(3x + a million) = sixty 5.4 log3.5^(3x + a million) = log65.4 (3x+a million)log 3.5 = log65.4 3xlog3.5 +log3.5 = log65.4 3xlog3.5 = log65.4 log3.5 x = (log65.4log3.5)/(3log3.5) sixteen^(x – 4) = 3^(3 – x) 5.7^(x – 2) = 5^x The final 2 issues are finished the comparable way with the aid of fact the 1st 3.