Rewrite each of these equations in logarithmic form if possi

Rewrite each of these equations in logarithmic form (if possible). If it is not possible, say why. 4^x = 64 5^x = 1/125 2^x = -32 We can rewrite any exponential equation in logarithmic form. Note that the input to the logarithmic function can only be no-negative real number. Rewrite the following exponential equations in logarithmic form. y = 4^x b = 1.5(5)^a m = 2^4t q = 3(5)^2t Without using your calculator, determine/estimate the value of the variable that makes the true. log_2 4 = y log_9(1/81) = t log_3(-2) = k log_5 10 = 5

Solution

2)

a)4^x=64

x=log₄ 64

b)5^x=1/125

x=log₅(1/125)

c)2^x=-32

not possible

logaritham is defined only for positive numbers

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3)

a)y=4^x

x=log₄y

b)b=1.5(5)^a

5^a=b/1.5

a=log₅(b/1.5)

c)m=2^4t

m=(2⁴)^t

m=16^t

t=log₁₆ m

d)q=3(5)^2k

q=3(5²)^k

q=3(25)^k

25^k=q/3

k=log₂₅(q/3)