Question

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

Answer 1

Answer:

x = 3.1

Step-by-step 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

$x = log_{10}(100 \times 12)$

Using the rules of logarithms

That's

$log_{a}(x \times y) = log_{a}(x) + log_{a}(y)$

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