What is the approximate value of x in the equation below? log₅(15) = x + 3

Solution:

Given, the equation Log₅(15) = x + 3.--- (1)

Using the logarithmic rule,

log₁₀(ab) = log₁₀a + log₁₀b

Log_b b = 1

Log₅15 = Log₅(5 × 3) = Log₅5 + Log₅3

Using logarithmic rule

Log₅15 = 1 + log₅3

Log₅3 = 0.682606

Log₅15 = 1 + 0.682606

= 1.682606

Substitute this value in (1)

1.682606 = x + 3

Subtract 3 from both sides we have,

1.682606 - 3 = x + 3 - 3

x = -1.317

Therefore, the approximate value of x is -1.317

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What is the approximate value of x in the equation below? log₅(15) = x + 3

Summary:

The approximate value of x in the equation below log₅(15) = x + 3 is -1.317