Name: Solving Exponential and Logarithmic Equations
Uploaded: 2019-07-19
Duration: 10 min 51 s
Description: In this video, we will learn the exponential and logarithmic equations and method of solving the exponential and logarithmic equations in a detailed manner.

Question

The variables $x$ and $y$ , satisfy the equation $5^{y} = 3^{2 x - 4}$ .

By taking natural logarithms, show that the graph of $y$ against $x$ , is a straight line and find the exact value of the gradient of this line.

Accepted Answer

Given the variables $x$ and $y$ , satisfy the equation $5^{y} = 3^{2 x - 4}$

Taking natural logarithms on both sides for $5^{y} = 3^{2 x - 4}$

$\Rightarrow \ln (5^{y}) = \ln (3^{2 x - 4})$

Use the power law of logarithms, $\ln {(u)}^{m} = m \ln (u)$

$\Rightarrow (y) \times \ln (5) = (2 x - 4) \times \ln (3)$

$\Rightarrow y = (\frac{(2 x) \times \ln (3)}{\ln (5)}) - \frac{4 \times \ln (3)}{\ln (5)}$

Above equation in the form of standard linear form as $Y = m X + c$ , so it is a straight line.

On comparing equation $y = (\frac{(2 x) \times \ln (3)}{\ln (5)}) - \frac{4 \times \ln (3)}{\ln (5)}$ with $Y = m X + c$ , we get gradient.

$\Rightarrow$ Gradient $m = \frac{2 \ln (3)}{\ln (5)}$

Therefore, gradient of the straight line is $m = \frac{2 \ln (3)}{\ln (5)}$ .

The variables $x$ and $y$ , satisfy the equation $5^{y} = 3^{2 x - 4}$ .

By taking natural logarithms, show that the graph of $y$ against $x$ , is a straight line and find the exact value of the gradient of this line.

Important Questions on Logarithmic and Exponential Functions

Learn and Prepare for any exam you want !

The variables x and y, satisfy the equation 5y=32x-4. By taking natural logarithms, show that the graph of y against x, is a straight line and find the exact value of the gradient of this line.

Important Questions on Logarithmic and Exponential Functions

Learn and Prepare for any exam you want !

The variables $x$ and $y$ , satisfy the equation $5^{y} = 3^{2 x - 4}$ .

By taking natural logarithms, show that the graph of $y$ against $x$ , is a straight line and find the exact value of the gradient of this line.