Question 161 Shikha has an order from a golf course designer to put palm trees through a - 23 machine and then through a - 33 machine- She thinks that she can do the job with a single repeater machine- What single repeater machine she should use-

The work done by hook up machine is equal to 2 × 2 × 2 × 3 × 3 × 3 × = 216 = 6^3 So, she should use (× 6^3) single machine for the purpose. ...

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Standard IX

Mathematics

Logarithms

Question 161 ...

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Question 161

Shikha has an order from a golf course designer to put palm trees through
a $(\times 2^{3})$ machine and then through $a (\times 3^{3})$ machine. She thinks that she can do the job with a single repeater machine. What single repeater machine she should use?

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Solution

The work done by hook-up machine is equal to $2 \times 2 \times 2 \times 3 \times 3 \times 3 \times = 216 = 6^{3}$
So, she should use $(\times 6^{3})$ single machine for the purpose.

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Question 161

Shikha has an order from a golf course designer to put palm trees through
a $(\times 2^{3})$ machine and then through $a (\times 3^{3})$ machine. She thinks that she can do the job with a single repeater machine. What single repeater machine she should use?

Question 159(i)

Find a single repeater machine that will do the same work as each hook-up.

Question 159(v)

Find a single repeater machine that will do the same work as each hook-up.

Question 153(ii)

In a repeater machine with 0 as an exponent, the base machine is applied 0 times.
What do you think the value of $6^{o}$ is ?
You have seen that a hook up of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression.
Asif Raza thought about how he could rewrite the expression $2^{2} 0 \times 2^{5}$ .

Asif Raza's idea is one of the product laws of exponents, which can be expressed like this
Multiplying Expressions with the same base $a^{b} \times a^{c} = a^{b + c}$
Actually, this law can be used with more than two expressions. As long as the bases are the same, to find the product you can add the exponents and use the same base.
e.g. $3^{2} \times 3^{3} \times 3^{10} = 3^{2 + 3 + 10} = 3^{15}$

Question 153(ii)

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Question 161 Shikha has an order from a golf course designer to put palm trees through a (×23) machine and then through a(×33) machine. She thinks that she can do the job with a single repeater machine. What single repeater machine she should use?

The work done by hook-up machine is equal to 2×2×2×3×3×3×=216=63 So, she should use (×63) single machine for the purpose.

Question 161

Shikha has an order from a golf course designer to put palm trees through
a $(\times 2^{3})$ machine and then through $a (\times 3^{3})$ machine. She thinks that she can do the job with a single repeater machine. What single repeater machine she should use?

The work done by hook-up machine is equal to $2 \times 2 \times 2 \times 3 \times 3 \times 3 \times = 216 = 6^{3}$
So, she should use $(\times 6^{3})$ single machine for the purpose.