Question

Express a in terms of b in the following:

`1/2 log a + 5 log b = 1`

Answer 1

Given: `1/2 log a + 5 log b = 1`

To find: Express a in terms of b.

Calculation:

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

`log a ^(1/2) + log b^5 = 1`

Step 2: Using the rule log m + log ⁡n = log ⁡(mn),

`log (a^(1/2) b^5) = 1`

Step 3: We know that log ⁡10 = 1  ....(Since base is 10.)

So, `log (a^(1/2) b^5) = log 10`

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

`a^(1/2) b^5 = 10`

Step 5: Divide both sides by b⁵:

`a^(1/2) = 10/b^5`

Now, square both sides:

a = `(10/b^5)^2`

a = `100/b^10`