# Solve the exponential equation 1/16=64^(4x-3) USING LOGARITHMS!!!!?

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Please show all work. Solve using logarithms!

• 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^(4x-3)

log(1/16) = log(64^(4x-3))

-log(16) = (4x-3) log(64)

-log(2^4) = (4x-3) log(2^6)

-4 log(2) = (4x-3) 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^(x-a million) = log 3 ^x (x-a million) log5 = x log 3 xlog5 -log 5 = xlog3 xlog5 -xlog3 = log 5 x(log5 -log3) = log 5 x = log5/(log5-log3) 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 = (log65.4-log3.5)/(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.

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