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Solve for x. Evaluate and round your answer to 1 decimal place(tenths place). 10x=1200

Solve for x. Evaluate and round your answer to 1 decimal place(tenths place). 10x-example-1

1 Answer

1 vote

Answer:

x = 3.1

Explanation:


{10}^(x) = 1200

To solve first take logarithm to both sides

That's


log_(10)(10) ^(x) = log_(10)(1200)


log_(10)(10)^(x) = x log_(10)(10)

But


log_(10)(10) = 1

So we have


x = log_(10)(1200)

Write 1200 as a number with the factor 100

That's

1200 = 100 × 12

So we have


x = log_(10)(100 * 12)

Using the rules of logarithms

That's


log_(a)(x * y) = log_(a)(x) + log_(a)(y)

Rewrite the expression

That's


x = log_(10)(100) + log_(10)(12)


x = log_(10)(10)^(2) + log_(10)(12)


x = 2 log_(10)(10) + log_(10)(12)


log_(10)(10) = 1


x = 2 + log_(10)(12)

x = 3.079

So we have the final answer as

x = 3.1 to one decimal place

Hope this helps you

User Raymond Ativie
by
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