Question

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

Answer 1

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