Question

Express a in terms of b in the following:

`2 log a - 1/3 log b = 2`

Answer 1

Given: `2 log a - 1/3 log b = 2`

To find: Express a in terms of b.

Calculation:

Step 1: Using the rule n log ⁡x = log ⁡xⁿ,

`log a^2  -  log b^(1/3) = 2`

Step 2: Using the rule log m − log ⁡n = `log ⁡(m/n)`,

`log (a^2/b^(1/3)) = 2`

Step 3: We know that 2 = log ⁡100  ....(Since the base is 10.)

So, `log (a^2/b^(1/3)) = log 100`

Step 4: Since the logarithms are equal, their arguments are equal:

`(a^2/b^(1/3)) = 100`

Step 5: Multiply both sides by `b^(1/3)`:

`a^2 = 100 b^(1/3)`

Now, take the square root of both sides:

a = `sqrt(100b^(1/3))`

a = `10b^(1/6)`