Easy Logarithmic Equation

Algebra Level 1

Let us define y y as:

y = log ⁡ 9 x + 1 \large y = \log_9 x + 1

Find the value of x x when y = 5 2 y = \dfrac{5}{2} .


The answer is 27.

Ram Mohith by Ram Mohith , 18, India

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2 solutions

y = log ⁡ 9 x + 1 For y = 5 2 5 2 = log ⁡ 9 x + 1 log ⁡ 9 = 5 2 − 1 = 3 2 x = 9 3 2 = 3 3 = 27 \begin{aligned} y & = \log_9 x + 1 & \small \color{#3D99F6} \text{For }y = \frac 52 \\ \frac 52 & = \log_9 x + 1 \\ \log_9 & = \frac 52-1 = \frac 32 \\ x & = 9^\frac 32 = 3^3 = \boxed{27} \end{aligned}

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Blan Morrison
Sep 15, 2018

2.5 = log ⁡ 9 x + 1 2.5=\log_9x+1 x = 9 1.5 = 9 3 x=9^{1.5}=\sqrt{9}^3 x = 3 3 = 27 x=3^3=27

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