Mathematics: Part a: if (6^2)^x = 1, what is the value of x? explain your answer. (5 points) part b: if (6^9)^x = 1, what are the possible values of x? explain your answer.

Part a: if (6^2)^x = 1, what is the value of x?

irosser215

10.03.2022

Part A: X=0

Part B: x=0

Step-by-step explanation:

Part A

(6^2)^X = 1

Applying the exponent rule: $(a^b)^c = a^{bc}$

So, our equation will become:

$6^{2X} = 1$

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

$ln(6^{2X}) =ln(1)$

We know, log(a^b) = b.loga Applying the rule,

$2Xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\2Xln6 =0\\Solving:\\X=0$

Part B

(6^9)^x = 1

Applying the exponent rule: $(a^b)^c = a^{bc}$

So, our equation will become:

$6^{9x} = 1$

We know if f(x) = g(x) then ln(f(x))= ln(g(x))

SO, taking natural logarithm ln on both sides and solving.

$ln(6^{9x}) =ln(1)$

We know, ln(a^b) = b.lna Applying the rule,

$9xln6 =ln(1)\\We\,\,know\,\,ln(1)=0\\9xln6 =0\\Solving:\\x=0$

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